diff --git a/dumux/assembly/boxlocalresidual.hh b/dumux/assembly/boxlocalresidual.hh
index eaadcedddf6ae9fd64388e42bb5e31f84f77775b..9f105cabc40ed8c3603efc35ede617f0fdb4f428 100644
--- a/dumux/assembly/boxlocalresidual.hh
+++ b/dumux/assembly/boxlocalresidual.hh
@@ -106,23 +106,21 @@ public:
             const auto& scv = fvGeometry.scv(scvf.insideScvIdx());
             const auto& bcTypes = elemBcTypes[scv.localDofIndex()];
 
-            // Neumann and Robin ("solution dependent Neumann") boundary conditions
-            if (bcTypes.hasNeumann() && !bcTypes.hasDirichlet())
+            // Treat Neumann and Robin ("solution dependent Neumann") boundary conditions.
+            // For Dirichlet there is no addition to the residual here but they
+            // are enforced strongly by replacing the residual entry afterwards.
+            if (bcTypes.hasNeumann())
             {
                 auto neumannFluxes = problem.neumann(element, fvGeometry, elemVolVars, scvf);
 
                 // multiply neumann fluxes with the area and the extrusion factor
                 neumannFluxes *= scvf.area()*elemVolVars[scv].extrusionFactor();
 
-                flux += neumannFluxes;
+                // only add fluxes to equations for which Neumann is set
+                for (int eqIdx = 0; eqIdx < NumEqVector::dimension; ++eqIdx)
+                    if (bcTypes.isNeumann(eqIdx))
+                        flux[eqIdx] += neumannFluxes[eqIdx];
             }
-
-            // for Dirichlet there is no addition to the residual here but they
-            // are enforced strongly by replacing the residual entry afterwards
-            else if (bcTypes.hasDirichlet() && !bcTypes.hasNeumann())
-                return flux;
-            else
-                DUNE_THROW(Dune::NotImplemented, "Mixed boundary conditions. Use pure boundary conditions by converting Dirichlet BCs to Robin BCs");
         }
 
         return flux;
diff --git a/test/geomechanics/elastic/problem.hh b/test/geomechanics/elastic/problem.hh
index 9762336500325cafcaa8139463a4420475def5b0..b8d2a4053cf0bf2a010e592fa70905928f1ca221 100644
--- a/test/geomechanics/elastic/problem.hh
+++ b/test/geomechanics/elastic/problem.hh
@@ -107,6 +107,39 @@ public:
     {
         BoundaryTypes values;
         values.setAllDirichlet();
+
+        if (globalPos[0] < eps_ && globalPos[1] > eps_ && globalPos[1] < 1.0 - eps_)
+            values.setNeumann(Indices::momentum(/*x-dir*/0));
+        if (globalPos[1] > 1.0 - eps_ && globalPos[0] > eps_ && globalPos[0] < 1.0 - eps_)
+            values.setNeumann(Indices::momentum(/*y-dir*/1));
+
+        return values;
+    }
+
+    NumEqVector neumann(const Element& element,
+                        const FVElementGeometry& fvGeometry,
+                        const ElementVolumeVariables& elemVolvars,
+                        const SubControlVolumeFace& scvf) const
+    {
+        GradU gradU = exactGradient(scvf.ipGlobal());
+
+        GradU epsilon;
+        for (int i = 0; i < dim; ++i)
+            for (int j = 0; j < dimWorld; ++j)
+                epsilon[i][j] = 0.5*(gradU[i][j] + gradU[j][i]);
+
+        const auto& lameParams = this->spatialParams().lameParamsAtPos(scvf.ipGlobal());
+        GradU sigma(0.0);
+        const auto traceEpsilon = trace(epsilon);
+        for (int i = 0; i < dim; ++i)
+        {
+            sigma[i][i] = lameParams.lambda()*traceEpsilon;
+            for (int j = 0; j < dimWorld; ++j)
+                sigma[i][j] += 2.0*lameParams.mu()*epsilon[i][j];
+        }
+
+        NumEqVector values;
+        sigma.mv(scvf.unitOuterNormal(), values);
         return values;
     }
 
diff --git a/test/references/elasticbox-reference.vtu b/test/references/elasticbox-reference.vtu
index 4a1cd64dddd8823444f82b8fd791d9c237103fb3..3199fcc9800a2964f648009ebc536bd02df8675a 100644
--- a/test/references/elasticbox-reference.vtu
+++ b/test/references/elasticbox-reference.vtu
@@ -4,36 +4,36 @@
     <Piece NumberOfCells="100" NumberOfPoints="121">
       <PointData Vectors="u">
         <DataArray type="Float32" Name="u" NumberOfComponents="3" format="ascii">
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         <DataArray type="Float32" Name="u_exact" NumberOfComponents="3" format="ascii">