diff --git a/src/GmshDiscreteModels.jl b/src/GmshDiscreteModels.jl
index 8339da7..f4b4150 100644
--- a/src/GmshDiscreteModels.jl
+++ b/src/GmshDiscreteModels.jl
@@ -175,6 +175,10 @@ function  _fill_connectivity!(
     i_lnode_to_node = nodeTags[j]
     if (nlnodes == d+1)
       _orient_simplex_connectivities!(nlnodes,i_lnode_to_node)
+    elseif (nlnodes == 4)
+      _sort_quad_connectivites!(nlnodes,i_lnode_to_node)
+    elseif (nlnodes == 8)
+      _sort_hex_connectivites!(nlnodes,i_lnode_to_node)
     end
     for (i,cell) in enumerate(i_to_cell)
       a = cell_to_nodes_prts[cell-o]-1
@@ -197,6 +201,26 @@ function _orient_simplex_connectivities!(nlnodes,i_lnode_to_node)
   end
 end
 
+function _sort_quad_connectivites!(nlnodes,i_lnode_to_node)
+  aux = zero(eltype(i_lnode_to_node))
+  offset = nlnodes-1
+  for i in 1:nlnodes:length(i_lnode_to_node)
+    aux = i_lnode_to_node[i+offset-1]
+    i_lnode_to_node[i+offset-1] = i_lnode_to_node[i+offset]
+    i_lnode_to_node[i+offset] = aux
+  end
+end
+
+function _sort_hex_connectivites!(nlnodes,i_lnode_to_node)
+  perm = [1, 2, 4, 3, 5, 6, 8, 7]
+  aux = zeros(eltype(i_lnode_to_node),nlnodes)
+  offset = nlnodes-1
+  for i in 1:nlnodes:length(i_lnode_to_node)
+    aux = i_lnode_to_node[i:i+offset]
+    i_lnode_to_node[i:i+offset] = aux[perm]
+  end
+end
+
 function _setup_reffes(gmsh,d)
 
   elemTypes, elemTags, nodeTags = gmsh.model.mesh.getElements(d)
diff --git a/test/GmshDiscreteModelsTests.jl b/test/GmshDiscreteModelsTests.jl
index 95e79aa..95b1e4f 100644
--- a/test/GmshDiscreteModelsTests.jl
+++ b/test/GmshDiscreteModelsTests.jl
@@ -15,4 +15,12 @@ mshfile = joinpath(@__DIR__,"..","demo","demo.msh")
 model = GmshDiscreteModel(mshfile)
 test_discrete_model(model)
 
+mshfile = joinpath(@__DIR__,"square.msh")
+model = GmshDiscreteModel(mshfile)
+test_discrete_model(model)
+
+mshfile = joinpath(@__DIR__,"cube.msh")
+model = GmshDiscreteModel(mshfile)
+test_discrete_model(model)
+
 end # module
diff --git a/test/cube.msh b/test/cube.msh
new file mode 100644
index 0000000..ac1ca9c
--- /dev/null
+++ b/test/cube.msh
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diff --git a/test/square.msh b/test/square.msh
new file mode 100644
index 0000000..02dc41e
--- /dev/null
+++ b/test/square.msh
@@ -0,0 +1,73 @@
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