diff --git a/src/BRepOffset/BRepOffset_MakeOffset_1.cxx b/src/BRepOffset/BRepOffset_MakeOffset_1.cxx
index 6462ea6348..de3239f7a1 100644
--- a/src/BRepOffset/BRepOffset_MakeOffset_1.cxx
+++ b/src/BRepOffset/BRepOffset_MakeOffset_1.cxx
@@ -304,6 +304,13 @@ static
                           const TopTools_IndexedMapOfShape& theMERemoved,
                           TopTools_IndexedMapOfShape& theInvEdges);
 
+static
+  void CheckEdgesCreatedByVertex (const TopTools_IndexedDataMapOfShapeListOfShape& theInvFaces,
+                                  const TopTools_DataMapOfShapeShape& theArtInvFaces,
+                                  const TopTools_DataMapOfShapeListOfShape& theEdgesOrigins,
+                                  const TopTools_IndexedMapOfShape& theValidEdges,
+                                  TopTools_IndexedMapOfShape& theInvEdges);
+
 static 
   void FindFacesToRebuild(const TopTools_IndexedDataMapOfShapeListOfShape&  theLFImages,
                           const TopTools_IndexedMapOfShape& theInvEdges,
@@ -1185,6 +1192,10 @@ void BuildSplitsOfFaces(const TopTools_ListOfShape& theLF,
   // filter invalid edges
   FilterInvalidEdges(theInvFaces, theArtInvFaces, aDMFMIE, aMERemoved, theInvEdges);
   //
+  // Check additionally validity of edges originated from vertices.
+  CheckEdgesCreatedByVertex (theInvFaces, theArtInvFaces, theEdgesOrigins,
+                             theValidEdges, theEdgesToAvoid);
+
 #ifdef OFFSET_DEBUG
   // show invalid edges
   TopoDS_Compound aCEInv;
@@ -3970,6 +3981,56 @@ void FilterInvalidFaces(TopTools_IndexedDataMapOfShapeListOfShape& theFImages,
   theInvFaces = aReallyInvFaces;
 }
 
+//=======================================================================
+//function : CheckEdgesCreatedByVertex
+//purpose  : Checks additionally the unchecked edges originated from vertices
+//=======================================================================
+void CheckEdgesCreatedByVertex (const TopTools_IndexedDataMapOfShapeListOfShape& theInvFaces,
+                                const TopTools_DataMapOfShapeShape& theArtInvFaces,
+                                const TopTools_DataMapOfShapeListOfShape& theEdgesOrigins,
+                                const TopTools_IndexedMapOfShape& theValidEdges,
+                                TopTools_IndexedMapOfShape& theInvEdges)
+{
+  // Mark the unchecked edges contained in invalid faces as invalid
+  const Standard_Integer aNbF = theInvFaces.Extent();
+  for (Standard_Integer i = 1; i <= aNbF; ++i)
+  {
+    const TopoDS_Shape& aF = theInvFaces.FindKey (i);
+    if (theArtInvFaces.IsBound (aF))
+      continue;
+
+    const TopTools_ListOfShape& aLFIm = theInvFaces (i);
+    for (TopTools_ListOfShape::Iterator it (aLFIm); it.More(); it.Next())
+    {
+      const TopoDS_Shape& aFIm = it.Value();
+      for (TopExp_Explorer expE (aFIm, TopAbs_EDGE); expE.More(); expE.Next())
+      {
+        const TopoDS_Shape& aE = expE.Current();
+        if (theInvEdges.Contains (aE)
+         || theValidEdges.Contains (aE))
+        {
+          continue;
+        }
+
+        // check if this edges is created by vertex
+        const TopTools_ListOfShape* pLEOr = theEdgesOrigins.Seek (aE);
+        if (!pLEOr)
+          continue;
+        TopTools_ListOfShape::Iterator itLEO (*pLEOr);
+        for (; itLEO.More(); itLEO.Next())
+        {
+          if (itLEO.Value().ShapeType() != TopAbs_VERTEX)
+            break;
+        }
+        if (!itLEO.More())
+        {
+          theInvEdges.Add (aE);
+        }
+      }
+    }
+  }
+}
+
 //=======================================================================
 //function : FilterInvalidEdges
 //purpose  : Filtering the invalid edges according to currently invalid faces
diff --git a/tests/offset/shape_type_i_c/XV1 b/tests/offset/shape_type_i_c/XV1
new file mode 100644
index 0000000000..0f47a790e7
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XV1
@@ -0,0 +1,20 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+restore [locate_data_file bug31542_trim.brep] s
+offsetparameter 1e-7 c i r
+offsetload s 0
+explode s f
+offsetonface s_3 8
+offsetonface s_2 2
+offsetonface s_10 2
+offsetperform result
+
+checkprops result -s 80331.8 -v 940931
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 12 -face 12 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XV2 b/tests/offset/shape_type_i_c/XV2
new file mode 100644
index 0000000000..3fed2d7bc6
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XV2
@@ -0,0 +1,20 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+restore [locate_data_file bug31542_trim.brep] s
+offsetparameter 1e-7 c i r
+offsetload s 0
+explode s f
+offsetonface s_3 8
+offsetonface s_2 2
+offsetonface s_10 5
+offsetperform result
+
+checkprops result -s 81322.5 -v 962242
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 13 -face 13 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XV3 b/tests/offset/shape_type_i_c/XV3
new file mode 100644
index 0000000000..4caf5686cc
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XV3
@@ -0,0 +1,20 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+restore [locate_data_file bug31542_trim.brep] s
+offsetparameter 1e-7 c i r
+offsetload s 0
+explode s f
+offsetonface s_3 8
+offsetonface s_2 5
+offsetonface s_10 2
+offsetperform result
+
+checkprops result -s 81322.5 -v 962242
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 13 -face 13 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XV4 b/tests/offset/shape_type_i_c/XV4
new file mode 100644
index 0000000000..ff4ea86880
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XV4
@@ -0,0 +1,20 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+restore [locate_data_file bug31542_trim.brep] s
+offsetparameter 1e-7 c i r
+offsetload s 0
+explode s f
+offsetonface s_3 10
+offsetonface s_2 5
+offsetonface s_10 5
+offsetperform result
+
+checkprops result -s 83093.5 -v 1.0107e+06
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 11 -face 11 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XV5 b/tests/offset/shape_type_i_c/XV5
new file mode 100644
index 0000000000..9fe074c981
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XV5
@@ -0,0 +1,18 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+restore [locate_data_file bug31542_trim.brep] s
+offsetparameter 1e-7 c i r
+offsetload s 0
+explode s f
+offsetonface s_9 7
+offsetperform result
+
+checkprops result -s 76756.9 -v 854480
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 14 -face 14 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XV6 b/tests/offset/shape_type_i_c/XV6
new file mode 100644
index 0000000000..d4982d04e7
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XV6
@@ -0,0 +1,18 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+restore [locate_data_file bug31542_trim.brep] s
+offsetparameter 1e-7 c i r
+offsetload s 0
+explode s f
+offsetonface s_9 15
+offsetperform result
+
+checkprops result -s 77082.5 -v 861875
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 15 -face 15 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XV7 b/tests/offset/shape_type_i_c/XV7
new file mode 100644
index 0000000000..cd4cf3780e
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XV7
@@ -0,0 +1,21 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+restore [locate_data_file bug31542_trim.brep] s
+offsetparameter 1e-7 c i r
+offsetload s 0
+explode s f
+offsetonface s_3 5
+offsetonface s_2 2
+offsetonface s_9 8
+offsetonface s_10 2
+offsetperform result
+
+checkprops result -s 78683.2 -v 908272
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 16 -face 16 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XV8 b/tests/offset/shape_type_i_c/XV8
new file mode 100644
index 0000000000..f2bd393b2f
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XV8
@@ -0,0 +1,45 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+set X1 5;  # positive x-axis
+set X2 10; # nagative x-axis
+set Y1 5;  # positive y-axis
+set Y2 10; # negative y-axis
+set TOP 0; # positive z-axis
+
+set eps 1.e-5
+
+restore [locate_data_file bug31542_trim.brep] s
+
+offsetparameter 1e-7 c i r
+offsetload s 0
+foreach f [explode s f] {
+  mksurface surf $f;
+  regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump surf] full x y z
+  if {[regexp "REVERSED" [whatis $f]]} {
+    set x [dval -1*$x];
+    set y [dval -1*$y];
+    set z [dval -1*$z];
+  }
+  if {$y < -1*$eps} {
+    offsetonface $f $Y2
+  } elseif {$y > $eps} {
+    offsetonface $f $Y1
+  } elseif {$x < -1*$eps} {
+    offsetonface $f $X2
+  } elseif {$x > $eps} {
+    offsetonface $f $X1
+  } elseif {$z > $eps} {
+    offsetonface $f $TOP
+  }
+}
+offsetperform result
+
+checkprops result -s 98415.4 -v 1.30965e+06
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 15 -face 15 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XV9 b/tests/offset/shape_type_i_c/XV9
new file mode 100644
index 0000000000..477b0b3caa
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XV9
@@ -0,0 +1,45 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+set X1 10; # positive x-axis
+set X2 5;  # nagative x-axis
+set Y1 10; # positive y-axis
+set Y2 5;  # negative y-axis
+set TOP 5; # positive z-axis
+
+set eps 1.e-5
+
+restore [locate_data_file bug31542_trim.brep] s
+
+offsetparameter 1e-7 c i r
+offsetload s 0
+foreach f [explode s f] {
+  mksurface surf $f;
+  regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump surf] full x y z
+  if {[regexp "REVERSED" [whatis $f]]} {
+    set x [dval -1*$x];
+    set y [dval -1*$y];
+    set z [dval -1*$z];
+  }
+  if {$y < -1*$eps} {
+    offsetonface $f $Y2
+  } elseif {$y > $eps} {
+    offsetonface $f $Y1
+  } elseif {$x < -1*$eps} {
+    offsetonface $f $X2
+  } elseif {$x > $eps} {
+    offsetonface $f $X1
+  } elseif {$z > $eps} {
+    offsetonface $f $TOP
+  }
+}
+offsetperform result
+
+checkprops result -s 99229.3 -v 1.33021e+06
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 16 -face 16 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XW1 b/tests/offset/shape_type_i_c/XW1
new file mode 100644
index 0000000000..ef85c767fb
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XW1
@@ -0,0 +1,45 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+set X1 10; # positive x-axis
+set X2 5;  # nagative x-axis
+set Y1 10; # positive y-axis
+set Y2 5;  # negative y-axis
+set TOP 5; # positive z-axis
+
+set eps 1.e-5
+
+restore [locate_data_file bug31542_dom-18777.input.brep] s
+
+offsetparameter 1e-7 c i r
+offsetload s 0
+foreach f [explode s f] {
+  mksurface surf $f;
+  regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump surf] full x y z
+  if {[regexp "REVERSED" [whatis $f]]} {
+    set x [dval -1*$x];
+    set y [dval -1*$y];
+    set z [dval -1*$z];
+  }
+  if {$y < -1*$eps} {
+    offsetonface $f $Y2
+  } elseif {$y > $eps} {
+    offsetonface $f $Y1
+  } elseif {$x < -1*$eps} {
+    offsetonface $f $X2
+  } elseif {$x > $eps} {
+    offsetonface $f $X1
+  } elseif {$z > $eps} {
+    offsetonface $f $TOP
+  }
+}
+offsetperform result
+
+checkprops result -s 705116 -v 2.26365e+07
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 32 -face 32 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XW2 b/tests/offset/shape_type_i_c/XW2
new file mode 100644
index 0000000000..7d122d280f
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XW2
@@ -0,0 +1,45 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+set X1 5;  # positive x-axis
+set X2 10; # nagative x-axis
+set Y1 5;  # positive y-axis
+set Y2 10; # negative y-axis
+set TOP 5; # positive z-axis
+
+set eps 1.e-5
+
+restore [locate_data_file bug31542_dom-18777.input.brep] s
+
+offsetparameter 1e-7 c i r
+offsetload s 0
+foreach f [explode s f] {
+  mksurface surf $f;
+  regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump surf] full x y z
+  if {[regexp "REVERSED" [whatis $f]]} {
+    set x [dval -1*$x];
+    set y [dval -1*$y];
+    set z [dval -1*$z];
+  }
+  if {$y < -1*$eps} {
+    offsetonface $f $Y2
+  } elseif {$y > $eps} {
+    offsetonface $f $Y1
+  } elseif {$x < -1*$eps} {
+    offsetonface $f $X2
+  } elseif {$x > $eps} {
+    offsetonface $f $X1
+  } elseif {$z > $eps} {
+    offsetonface $f $TOP
+  }
+}
+offsetperform result
+
+checkprops result -s 705116 -v 2.26365e+07
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 32 -face 32 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XW3 b/tests/offset/shape_type_i_c/XW3
new file mode 100644
index 0000000000..616fe86b6e
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XW3
@@ -0,0 +1,45 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+set X1 5;  # positive x-axis
+set X2 5;  # nagative x-axis
+set Y1 10; # positive y-axis
+set Y2 10; # negative y-axis
+set TOP 5; # positive z-axis
+
+set eps 1.e-5
+
+restore [locate_data_file bug31542_dom-18777.input.brep] s
+
+offsetparameter 1e-7 c i r
+offsetload s 0
+foreach f [explode s f] {
+  mksurface surf $f;
+  regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump surf] full x y z
+  if {[regexp "REVERSED" [whatis $f]]} {
+    set x [dval -1*$x];
+    set y [dval -1*$y];
+    set z [dval -1*$z];
+  }
+  if {$y < -1*$eps} {
+    offsetonface $f $Y2
+  } elseif {$y > $eps} {
+    offsetonface $f $Y1
+  } elseif {$x < -1*$eps} {
+    offsetonface $f $X2
+  } elseif {$x > $eps} {
+    offsetonface $f $X1
+  } elseif {$z > $eps} {
+    offsetonface $f $TOP
+  }
+}
+offsetperform result
+
+checkprops result -s 705089 -v 2.27281e+07
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 32 -face 32 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XW4 b/tests/offset/shape_type_i_c/XW4
new file mode 100644
index 0000000000..ede5f3ee35
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XW4
@@ -0,0 +1,45 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+set X1 10; # positive x-axis
+set X2 10; # nagative x-axis
+set Y1 5;  # positive y-axis
+set Y2 5;  # negative y-axis
+set TOP 5; # positive z-axis
+
+set eps 1.e-5
+
+restore [locate_data_file bug31542_dom-18777.input.brep] s
+
+offsetparameter 1e-7 c i r
+offsetload s 0
+foreach f [explode s f] {
+  mksurface surf $f;
+  regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump surf] full x y z
+  if {[regexp "REVERSED" [whatis $f]]} {
+    set x [dval -1*$x];
+    set y [dval -1*$y];
+    set z [dval -1*$z];
+  }
+  if {$y < -1*$eps} {
+    offsetonface $f $Y2
+  } elseif {$y > $eps} {
+    offsetonface $f $Y1
+  } elseif {$x < -1*$eps} {
+    offsetonface $f $X2
+  } elseif {$x > $eps} {
+    offsetonface $f $X1
+  } elseif {$z > $eps} {
+    offsetonface $f $TOP
+  }
+}
+offsetperform result
+
+checkprops result -s 703838 -v 2.25528e+07
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 30 -face 30 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XW5 b/tests/offset/shape_type_i_c/XW5
new file mode 100644
index 0000000000..cbf7a46f6c
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XW5
@@ -0,0 +1,45 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+set X1 5;  # positive x-axis
+set X2 10; # nagative x-axis
+set Y1 5;  # positive y-axis
+set Y2 10; # negative y-axis
+set TOP 0; # positive z-axis
+
+set eps 1.e-5
+
+restore [locate_data_file bug31542_dom-18777.input.brep] s
+
+offsetparameter 1e-7 c i r
+offsetload s 0
+foreach f [explode s f] {
+  mksurface surf $f;
+  regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump surf] full x y z
+  if {[regexp "REVERSED" [whatis $f]]} {
+    set x [dval -1*$x];
+    set y [dval -1*$y];
+    set z [dval -1*$z];
+  }
+  if {$y < -1*$eps} {
+    offsetonface $f $Y2
+  } elseif {$y > $eps} {
+    offsetonface $f $Y1
+  } elseif {$x < -1*$eps} {
+    offsetonface $f $X2
+  } elseif {$x > $eps} {
+    offsetonface $f $X1
+  } elseif {$z > $eps} {
+    offsetonface $f $TOP
+  }
+}
+offsetperform result
+
+checkprops result -s 702224 -v 2.17722e+07
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 28 -face 28 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XW6 b/tests/offset/shape_type_i_c/XW6
new file mode 100644
index 0000000000..fe7f780227
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XW6
@@ -0,0 +1,45 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+set X1 10; # positive x-axis
+set X2 5;  # nagative x-axis
+set Y1 10; # positive y-axis
+set Y2 5;  # negative y-axis
+set TOP 0; # positive z-axis
+
+set eps 1.e-5
+
+restore [locate_data_file bug31542_dom-18777.input.brep] s
+
+offsetparameter 1e-7 c i r
+offsetload s 0
+foreach f [explode s f] {
+  mksurface surf $f;
+  regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump surf] full x y z
+  if {[regexp "REVERSED" [whatis $f]]} {
+    set x [dval -1*$x];
+    set y [dval -1*$y];
+    set z [dval -1*$z];
+  }
+  if {$y < -1*$eps} {
+    offsetonface $f $Y2
+  } elseif {$y > $eps} {
+    offsetonface $f $Y1
+  } elseif {$x < -1*$eps} {
+    offsetonface $f $X2
+  } elseif {$x > $eps} {
+    offsetonface $f $X1
+  } elseif {$z > $eps} {
+    offsetonface $f $TOP
+  }
+}
+offsetperform result
+
+checkprops result -s 702224 -v 2.17722e+07
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 28 -face 28 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XW7 b/tests/offset/shape_type_i_c/XW7
new file mode 100644
index 0000000000..d195a55a88
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XW7
@@ -0,0 +1,45 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+set X1 10;  # positive x-axis
+set X2 5;   # nagative x-axis
+set Y1 10;  # positive y-axis
+set Y2 5;   # negative y-axis
+set TOP 10; # positive z-axis
+
+set eps 1.e-5
+
+restore [locate_data_file bug31542_dom-18777.input.brep] s
+
+offsetparameter 1e-7 c i r
+offsetload s 0
+foreach f [explode s f] {
+  mksurface surf $f;
+  regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump surf] full x y z
+  if {[regexp "REVERSED" [whatis $f]]} {
+    set x [dval -1*$x];
+    set y [dval -1*$y];
+    set z [dval -1*$z];
+  }
+  if {$y < -1*$eps} {
+    offsetonface $f $Y2
+  } elseif {$y > $eps} {
+    offsetonface $f $Y1
+  } elseif {$x < -1*$eps} {
+    offsetonface $f $X2
+  } elseif {$x > $eps} {
+    offsetonface $f $X1
+  } elseif {$z > $eps} {
+    offsetonface $f $TOP
+  }
+}
+offsetperform result
+
+checkprops result -s 709138 -v 2.35754e+07
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 31 -face 31 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XW8 b/tests/offset/shape_type_i_c/XW8
new file mode 100644
index 0000000000..b1cd49b94b
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XW8
@@ -0,0 +1,16 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+restore [locate_data_file bug31542_dom-18777.input.brep] s
+offsetparameter 1e-7 c i r
+offsetload s 10
+offsetperform result
+
+checkprops result -s 747800 -v 2.65246e+07
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 30 -face 30 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/offset/shape_type_i_c/XW9 b/tests/offset/shape_type_i_c/XW9
new file mode 100644
index 0000000000..8306abe87e
--- /dev/null
+++ b/tests/offset/shape_type_i_c/XW9
@@ -0,0 +1,16 @@
+puts "========"
+puts "0031542: Modeling Algorithms - Offset algorithm produces incomplete result in mode Complete join type Intersection"
+puts "========"
+puts ""
+
+restore [locate_data_file bug31542_dom-18777.input.brep] s
+offsetparameter 1e-7 c i r
+offsetload s 15
+offsetperform result
+
+checkprops result -s 799301 -v 3.0392e+07
+
+unifysamedom result_unif result
+checknbshapes result_unif -wire 34 -face 34 -shell 1 -solid 1
+
+checkview -display result_unif -2d -path ${imagedir}/${test_image}.png