diff --git a/cpp/demos/meshtie/main.cpp b/cpp/demos/meshtie/main.cpp
index 27bc3f41..e3d38dff 100644
--- a/cpp/demos/meshtie/main.cpp
+++ b/cpp/demos/meshtie/main.cpp
@@ -173,11 +173,12 @@ int main(int argc, char* argv[])
     auto contact_markers
         = std::make_shared<dolfinx::graph::AdjacencyList<std::int32_t>>(
             std::move(data), std::move(offsets));
-    std::vector<std::shared_ptr<dolfinx::mesh::MeshTags<std::int32_t>>> markers
+    std::vector<std::shared_ptr<const dolfinx::mesh::MeshTags<std::int32_t>>>
+        markers
         = {std::make_shared<dolfinx::mesh::MeshTags<std::int32_t>>(facet1)};
     std::vector<std::array<int, 2>> pairs = {{0, 1}, {1, 0}};
     auto meshties
-        = dolfinx_contact::MeshTie(markers, contact_markers, pairs, mesh, 5);
+        = dolfinx_contact::MeshTie(markers, *contact_markers, pairs, mesh, 5);
 
     meshties.generate_kernel_data(dolfinx_contact::Problem::Elasticity, *V,
                                   {{"mu", mu}, {"lambda", lmbda}}, E * gamma,
diff --git a/cpp/demos/meshtieHeatEquation/main.cpp b/cpp/demos/meshtieHeatEquation/main.cpp
index 0c5f1e61..4d0666e4 100644
--- a/cpp/demos/meshtieHeatEquation/main.cpp
+++ b/cpp/demos/meshtieHeatEquation/main.cpp
@@ -105,11 +105,12 @@ int main(int argc, char* argv[])
     auto contact_markers
         = std::make_shared<dolfinx::graph::AdjacencyList<std::int32_t>>(
             std::move(data), std::move(offsets));
-    std::vector<std::shared_ptr<dolfinx::mesh::MeshTags<std::int32_t>>> markers
+    std::vector<std::shared_ptr<const dolfinx::mesh::MeshTags<std::int32_t>>>
+        markers
         = {std::make_shared<dolfinx::mesh::MeshTags<std::int32_t>>(facet1)};
     std::vector<std::array<int, 2>> pairs = {{0, 1}, {1, 0}};
     auto meshties
-        = dolfinx_contact::MeshTie(markers, contact_markers, pairs, mesh, 5);
+        = dolfinx_contact::MeshTie(markers, *contact_markers, pairs, mesh, 5);
 
     meshties.generate_kernel_data(dolfinx_contact::Problem::Poisson, *Q,
                                   {{"kdt", kdt}}, gamma, theta);
diff --git a/cpp/demos/meshtieHeatTransfer/main.cpp b/cpp/demos/meshtieHeatTransfer/main.cpp
index 8e30a8ff..afb00cb4 100644
--- a/cpp/demos/meshtieHeatTransfer/main.cpp
+++ b/cpp/demos/meshtieHeatTransfer/main.cpp
@@ -257,14 +257,15 @@ int main(int argc, char* argv[])
         = std::make_shared<dolfinx::graph::AdjacencyList<std::int32_t>>(
             std::move(data), std::move(offsets));
     // wrap facet markers
-    std::vector<std::shared_ptr<dolfinx::mesh::MeshTags<std::int32_t>>> markers
+    std::vector<std::shared_ptr<const dolfinx::mesh::MeshTags<std::int32_t>>>
+        markers
         = {std::make_shared<dolfinx::mesh::MeshTags<std::int32_t>>(facet1)};
     // define pairs (slave, master)
     std::vector<std::array<int, 2>> pairs = {{0, 1}, {1, 0}};
 
     // create meshties
     auto meshties = std::make_shared<dolfinx_contact::MeshTie>(
-        dolfinx_contact::MeshTie(markers, contact_markers, pairs, mesh, 5));
+        dolfinx_contact::MeshTie(markers, *contact_markers, pairs, mesh, 5));
 
     // Nitsche parameters
     double gamma = 10;
diff --git a/cpp/demos/meshtieNewton/main.cpp b/cpp/demos/meshtieNewton/main.cpp
index 65a86b73..3b482146 100644
--- a/cpp/demos/meshtieNewton/main.cpp
+++ b/cpp/demos/meshtieNewton/main.cpp
@@ -331,14 +331,15 @@ int main(int argc, char* argv[])
         = std::make_shared<dolfinx::graph::AdjacencyList<std::int32_t>>(
             std::move(data), std::move(offsets));
     // wrap facet markers
-    std::vector<std::shared_ptr<dolfinx::mesh::MeshTags<std::int32_t>>> markers
+    std::vector<std::shared_ptr<const dolfinx::mesh::MeshTags<std::int32_t>>>
+        markers
         = {std::make_shared<dolfinx::mesh::MeshTags<std::int32_t>>(facet1)};
     // define pairs (slave, master)
     std::vector<std::array<int, 2>> pairs = {{0, 1}, {1, 0}};
 
     // create meshties
     auto meshties = std::make_shared<dolfinx_contact::MeshTie>(
-        dolfinx_contact::MeshTie(markers, contact_markers, pairs, mesh, 5));
+        dolfinx_contact::MeshTie(markers, *contact_markers, pairs, mesh, 5));
 
     // create "non-linear" meshtie problem (linear problem written as non-linear
     // problem)