diff --git a/reframe_tests/regression_checks/TestConeGeometry_4c12b6bd/partial_cone.h5 b/reframe_tests/regression_checks/TestConeGeometry_111aa52c/non_axis_aligned_cone.h5
similarity index 100%
rename from reframe_tests/regression_checks/TestConeGeometry_4c12b6bd/partial_cone.h5
rename to reframe_tests/regression_checks/TestConeGeometry_111aa52c/non_axis_aligned_cone.h5
diff --git a/reframe_tests/regression_checks/TestConeGeometry_7e7be83a/overtall_cone.h5 b/reframe_tests/regression_checks/TestConeGeometry_7e7be83a/overtall_cone.h5
new file mode 100644
index 00000000..ec82deda
Binary files /dev/null and b/reframe_tests/regression_checks/TestConeGeometry_7e7be83a/overtall_cone.h5 differ
diff --git a/reframe_tests/regression_checks/TestConeGeometry_ca15ee64/rigid_cone.h5 b/reframe_tests/regression_checks/TestConeGeometry_ca15ee64/rigid_cone.h5
new file mode 100644
index 00000000..e3964cd2
Binary files /dev/null and b/reframe_tests/regression_checks/TestConeGeometry_ca15ee64/rigid_cone.h5 differ
diff --git a/reframe_tests/tests/src/geometry_tests/cone_geometry/partial_cone.in b/reframe_tests/tests/src/geometry_tests/cone_geometry/non_axis_aligned_cone.in
similarity index 100%
rename from reframe_tests/tests/src/geometry_tests/cone_geometry/partial_cone.in
rename to reframe_tests/tests/src/geometry_tests/cone_geometry/non_axis_aligned_cone.in
diff --git a/reframe_tests/tests/src/geometry_tests/cone_geometry/overtall_cone.in b/reframe_tests/tests/src/geometry_tests/cone_geometry/overtall_cone.in
new file mode 100644
index 00000000..066fef07
--- /dev/null
+++ b/reframe_tests/tests/src/geometry_tests/cone_geometry/overtall_cone.in
@@ -0,0 +1,11 @@
+#title: Hertzian dipole over a half-space
+#domain: 0.100 0.100 0.100
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 3e-9
+
+#waveform: gaussiandot 1 1e9 myWave
+#hertzian_dipole: z 0.020 0.020 0.020 myWave
+#rx: 0.080 0.080 0.080
+
+#material: 8 0 1 0 half_space
+#cone: 0 0.05 0.05 0.150 0.05 0.05 0.05 0 half_space
diff --git a/reframe_tests/tests/src/geometry_tests/cone_geometry/rigid_cone.in b/reframe_tests/tests/src/geometry_tests/cone_geometry/rigid_cone.in
new file mode 100644
index 00000000..071914da
--- /dev/null
+++ b/reframe_tests/tests/src/geometry_tests/cone_geometry/rigid_cone.in
@@ -0,0 +1,11 @@
+#title: Hertzian dipole over a half-space
+#domain: 0.100 0.100 0.100
+#dx_dy_dz: 0.001 0.001 0.001
+#time_window: 3e-9
+
+#waveform: gaussiandot 1 1e9 myWave
+#hertzian_dipole: z 0.020 0.020 0.020 myWave
+#rx: 0.080 0.080 0.080
+
+#material: 8 0 1 0 half_space
+#cone: 0 0.05 0.05 0.100 0.05 0.05 0.05 0 half_space n
diff --git a/reframe_tests/tests/test_geometry.py b/reframe_tests/tests/test_geometry.py
index 3bb02c7f..be4b4832 100644
--- a/reframe_tests/tests/test_geometry.py
+++ b/reframe_tests/tests/test_geometry.py
@@ -38,7 +38,9 @@ class TestBoxGeometryNoPml(GprMaxRegressionTest):
 class TestConeGeometry(GprMaxRegressionTest):
     tags = {"test", "serial", "geometery", "cone"}
     sourcesdir = "src/geometry_tests/cone_geometry"
-    model = parameter(["full_cone", "small_cone", "partial_cone"])
+    model = parameter(
+        ["full_cone", "small_cone", "non_axis_aligned_cone", "overtall_cone", "rigid_cone"]
+    )
 
 
 @rfm.simple_test