diff --git a/src/user/user_mesh.cc b/src/user/user_mesh.cc
index c85e3cd9..db09b8fb 100644
--- a/src/user/user_mesh.cc
+++ b/src/user/user_mesh.cc
@@ -1637,7 +1637,7 @@ void mjCMesh::CheckMesh(mjtGeomInertia type) {
   if (!processed_) {
     return;
   }
-  if (invalidorientation_.first>=0 || invalidorientation_.second>=0)
+  if ((invalidorientation_.first>=0 || invalidorientation_.second>=0) && model->exactmeshinertia)
     throw mjCError(this,
                    "faces of mesh '%s' have inconsistent orientation. Please check the "
                    "faces containing the vertices %d and %d.",
diff --git a/test/user/user_mesh_test.cc b/test/user/user_mesh_test.cc
index 845dbba6..1eaaa0e1 100644
--- a/test/user/user_mesh_test.cc
+++ b/test/user/user_mesh_test.cc
@@ -464,19 +464,19 @@ TEST_F(MjCMeshTest, TinyInertiaFails) {
           "mass and inertia of moving bodies must be larger than mjMINVAL"));
 }
 
-TEST_F(MjCMeshTest, MalformedFaceFails) {
+TEST_F(MjCMeshTest, FlippedFaceAllowedInexactInertia) {
   const std::string xml_path = GetTestDataFilePath(kMalformedFaceOBJPath);
   std::array<char, 1024> error;
   mjModel* model = mj_loadXML(xml_path.c_str(), 0, error.data(), error.size());
-  EXPECT_THAT(model, testing::IsNull());
-  EXPECT_THAT(error.data(), HasSubstr(
-        "Error: faces of mesh 'malformed_face' have inconsistent orientation. "
-        "Please check the faces containing the vertices 1 and 2."));
+  EXPECT_THAT(model, testing::NotNull());
+  EXPECT_THAT(model->nmeshface, 4);
+  mj_deleteModel(model);
 }
 
-TEST_F(MjCMeshTest, FlippedFaceFails) {
+TEST_F(MjCMeshTest, FlippedFaceFailsExactInertia) {
   static constexpr char xml[] = R"(
   <mujoco>
+    <compiler exactmeshinertia="true"/>
     <asset>
       <mesh name="example_mesh"
         vertex="0 0 0  1 0 0  0 1 0  0 0 1"