diff --git a/test/test_model/patch_tests/patch_test_linear_anisotropic_explicit.py b/test/test_model/patch_tests/patch_test_linear_anisotropic_explicit.py
new file mode 100644
index 000000000..3693239fd
--- /dev/null
+++ b/test/test_model/patch_tests/patch_test_linear_anisotropic_explicit.py
@@ -0,0 +1,72 @@
+#!/usr/bin/env python3
+
+from patch_test_linear_solid_mechanics_fixture import TestPatchTestSMMLinear
+import akantu
+import unittest
+import numpy as np
+
+# Stiffness tensor, rotated by hand
+C = np.array([[[[112.93753505, 1.85842452538e-10, -4.47654358027e-10],
+               [1.85847317471e-10, 54.2334345331, -3.69840984824],
+               [-4.4764768395e-10, -3.69840984824, 56.848605217]],
+              [[1.85847781609e-10, 25.429294233, -3.69840984816],
+               [25.429294233, 3.31613847493e-10, -8.38797920011e-11],
+               [-3.69840984816, -8.38804581349e-11, -1.97875715813e-10]],
+              [[-4.47654358027e-10, -3.69840984816, 28.044464917],
+               [-3.69840984816, 2.09374961813e-10, 9.4857455224e-12],
+               [28.044464917, 9.48308098714e-12, -2.1367885239e-10]]],
+             [[[1.85847781609e-10, 25.429294233, -3.69840984816],
+               [25.429294233, 3.31613847493e-10, -8.38793479119e-11],
+               [-3.69840984816, -8.38795699565e-11, -1.97876381947e-10]],
+              [[54.2334345331, 3.31617400207e-10, 2.09372075233e-10],
+               [3.3161562385e-10, 115.552705733, -3.15093728886e-10],
+               [2.09372075233e-10, -3.15090176173e-10, 54.2334345333]],
+              [[-3.69840984824, -8.38795699565e-11, 9.48219280872e-12],
+               [-8.38795699565e-11, -3.1509195253e-10, 25.4292942335],
+               [9.48441325477e-12, 25.4292942335, 3.69840984851]]],
+             [[[-4.47653469848e-10, -3.69840984816, 28.044464917],
+               [-3.69840984816, 2.09374073634e-10, 9.48752187924e-12],
+               [28.044464917, 9.48552347779e-12, -2.1367885239e-10]],
+              [[-3.69840984824, -8.3884899027e-11, 9.48219280872e-12],
+               [-8.3884899027e-11, -3.150972816e-10, 25.4292942335],
+               [9.48041645188e-12, 25.4292942335, 3.69840984851]],
+              [[56.848605217, -1.97875493768e-10, -2.13681516925e-10],
+               [-1.97877270125e-10, 54.2334345333, 3.69840984851],
+               [-2.13683293282e-10, 3.69840984851, 112.93753505]]]])
+
+
+def foo(self):
+
+    self.initModel(akantu._explicit_lumped_mass, "material_anisotropic.dat")
+
+    coordinates = self.mesh.getNodes()
+    displacement = self.model.getDisplacement()
+
+    # set the position of all nodes to the static solution
+    self.setLinearDOF(displacement, coordinates)
+
+    for s in range(0, 100):
+        self.model.solveStep()
+
+    ekin = self.model.getEnergy("kinetic")
+    self.assertAlmostEqual(0, ekin, delta=1e-16)
+
+    self.checkDisplacements()
+    self.checkStrains()
+
+    def foo(pstrain):
+        strain = (pstrain + pstrain.transpose()) / 2.
+        stress = np.zeros((self.dim, self.dim))
+
+        for i in range(0, self.dim):
+            for j in range(0, self.dim):
+                stress[i, j] = 0
+                for k in range(0, self.dim):
+                    for l in range(0, self.dim):
+                        stress[i, j] += C[i][j][k][l] * strain(k, l)
+        return stress
+    self.checkStresses(foo)
+
+
+suite = TestPatchTestSMMLinear.TYPED_TEST(foo, "AnisotropicExplicit")
+unittest.TextTestRunner(verbosity=1).run(suite)
diff --git a/test/test_model/patch_tests/patch_test_linear_elastic_explicit.py b/test/test_model/patch_tests/patch_test_linear_elastic_explicit.py
new file mode 100644
index 000000000..7ea90b917
--- /dev/null
+++ b/test/test_model/patch_tests/patch_test_linear_elastic_explicit.py
@@ -0,0 +1,27 @@
+#!/usr/bin/env python3
+
+from patch_test_linear_solid_mechanics_fixture import TestPatchTestSMMLinear
+import akantu
+import unittest
+
+def foo(self):
+    filename = "material_check_stress_plane_stress.dat"
+    if self.plane_strain:
+        filename = "material_check_stress_plane_strain.dat"
+
+    self.initModel(akantu._explicit_lumped_mass, filename)
+
+    coordinates = self.mesh.getNodes()
+    displacement = self.model.getDisplacement()
+    # set the position of all nodes to the static solution
+    self.setLinearDOF(displacement, coordinates)
+
+    for s in range(0, 100):
+            self.model.solveStep()
+
+    ekin = self.model.getEnergy("kinetic")
+    self.assertAlmostEqual(0, ekin, 1e-16)
+    self.checkAll()
+
+
+TestPatchTestSMMLinear.TYPED_TEST(foo, "Explicit")