diff --git a/src/StdSelect/StdSelect_BRepSelectionTool.cxx b/src/StdSelect/StdSelect_BRepSelectionTool.cxx
index 5b72c7507d..bcf81e6917 100644
--- a/src/StdSelect/StdSelect_BRepSelectionTool.cxx
+++ b/src/StdSelect/StdSelect_BRepSelectionTool.cxx
@@ -637,8 +637,6 @@ Standard_Boolean StdSelect_BRepSelectionTool::GetSensitiveForFace (const TopoDS_
         const gp_Cone aCone = BRepAdaptor_Surface (theFace).Cone();
 
         gp_Trsf aTrsf;
-        aTrsf.SetTransformation (aCone.Position(), gp::XOY());
-
         Standard_Real aRad1;
         Standard_Real aRad2;
         Standard_Real aHeight;
@@ -647,14 +645,18 @@ Standard_Boolean StdSelect_BRepSelectionTool::GetSensitiveForFace (const TopoDS_
           aRad1 = 0.0;
           aRad2 = aCircles.First().Radius();
           aHeight = aRad2 * Tan (aCone.SemiAngle());
+          aTrsf.SetTransformation (aCone.Position(), gp::XOY());
         }
         else
         {
-          aRad1 = aCone.RefRadius();
-          aRad2 = IsEqual (aRad1, aCircles.First().Radius()) 
-            ? aCircles.Last().Radius()
-            : aCircles.First().Radius();
+          aRad1 = aCircles.First().Radius();
+          aRad2 = aCircles.Last().Radius();
           aHeight = aCircles.First().Location().Distance (aCircles.Last().Location());
+
+          const gp_Pnt aPos = aCircles.First().Location();
+          const gp_Dir aDirection (aCircles.Last().Location().XYZ() - aPos.XYZ());
+
+          aTrsf.SetTransformation (gp_Ax3(aPos, aDirection), gp::XOY());
         }
 
         Handle(Select3D_SensitiveCylinder) aSensSCyl = new Select3D_SensitiveCylinder (theOwner, aRad1, aRad2, aHeight, aTrsf, true);
diff --git a/tests/v3d/bugs/bug33664 b/tests/v3d/bugs/bug33664_1
similarity index 88%
rename from tests/v3d/bugs/bug33664
rename to tests/v3d/bugs/bug33664_1
index 969ff42131..445cc692f7 100644
--- a/tests/v3d/bugs/bug33664
+++ b/tests/v3d/bugs/bug33664_1
@@ -18,4 +18,4 @@ if {[vnbselected] != "1"} {
 }
 
 vselect 0 0
-vdump $::imagedir/${::casename}.png
+vdump $::imagedir/${::casename}_cylinder.png
diff --git a/tests/v3d/bugs/bug33664_2 b/tests/v3d/bugs/bug33664_2
new file mode 100644
index 0000000000..ed1cbf622a
--- /dev/null
+++ b/tests/v3d/bugs/bug33664_2
@@ -0,0 +1,36 @@
+puts "============"
+puts "0033664: Visualization - Selection does not work for simple shape"
+puts "============"
+puts ""
+
+pload MODELING VISUALIZATION
+vclear
+vinit View1
+
+pcone c1 50 100 100
+ttranslate c1 100 0 100
+explode c1
+explode c1_1
+
+pcone c2 100 50 100
+ttranslate c2 -100 0 100
+explode c2
+explode c2_1
+
+pcone c3 0 100 100
+ttranslate c3 100 0 -100
+explode c3
+explode c3_1
+
+pcone c4 100 0 100
+ttranslate c4 -100 0 -100
+explode c4
+explode c4_1
+
+vdisplay c1_1_1 c2_1_1 c3_1_1 c4_1_1 -dispmode 1
+vsensdis
+
+vfront
+vfit
+
+vdump $::imagedir/${::casename}_cone.png