diff --git a/tests/regression_tests/filter_mesh/inputs_true.dat b/tests/regression_tests/filter_mesh/inputs_true.dat
index 37716c02e..38b20b7e3 100644
--- a/tests/regression_tests/filter_mesh/inputs_true.dat
+++ b/tests/regression_tests/filter_mesh/inputs_true.dat
@@ -53,36 +53,58 @@
     <y_grid>-7.5 -6.617647058823529 -5.735294117647059 -4.852941176470589 -3.9705882352941178 -3.0882352941176467 -2.2058823529411766 -1.3235294117647065 -0.4411764705882355 0.4411764705882355 1.3235294117647065 2.2058823529411757 3.0882352941176467 3.9705882352941178 4.852941176470587 5.735294117647058 6.617647058823529 7.5</y_grid>
     <z_grid>1.0 1.223224374241637 1.4962778697388448 1.8302835609029084 2.2388474634702153 2.7386127875258306 3.3499379133114306 4.09772570775871 5.012437964687018 6.131336292779302 7.500000000000001</z_grid>
   </mesh>
+  <mesh id="5" type="cylindrical">
+    <r_grid>0.0 0.4411764705882353 0.8823529411764706 1.3235294117647058 1.7647058823529411 2.2058823529411766 2.6470588235294117 3.0882352941176467 3.5294117647058822 3.9705882352941178 4.411764705882353 4.852941176470588 5.294117647058823 5.735294117647059 6.1764705882352935 6.617647058823529 7.0588235294117645 7.5</r_grid>
+    <p_grid>0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 200.0 220.0 240.0 260.0 280.0 300.0 320.0 340.0 360.0</p_grid>
+    <z_grid>-7.5 -6.5625 -5.625 -4.6875 -3.75 -2.8125 -1.875 -0.9375 0.0 0.9375 1.875 2.8125 3.75 4.6875 5.625 6.5625 7.5</z_grid>
+  </mesh>
+  <mesh id="6" type="spherical">
+    <r_grid>0.0 0.4411764705882353 0.8823529411764706 1.3235294117647058 1.7647058823529411 2.2058823529411766 2.6470588235294117 3.0882352941176467 3.5294117647058822 3.9705882352941178 4.411764705882353 4.852941176470588 5.294117647058823 5.735294117647059 6.1764705882352935 6.617647058823529 7.0588235294117645 7.5</r_grid>
+    <t_grid>0.0 22.5 45.0 67.5 90.0 112.5 135.0 157.5 180.0</t_grid>
+    <p_grid>0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 200.0 220.0 240.0 260.0 280.0 300.0 320.0 340.0 360.0</p_grid>
+  </mesh>
   <filter id="1" type="mesh">
     <bins>1</bins>
   </filter>
-  <filter id="5" type="meshsurface">
+  <filter id="7" type="meshsurface">
     <bins>1</bins>
   </filter>
   <filter id="2" type="mesh">
     <bins>2</bins>
   </filter>
-  <filter id="6" type="meshsurface">
+  <filter id="8" type="meshsurface">
     <bins>2</bins>
   </filter>
   <filter id="3" type="mesh">
     <bins>3</bins>
   </filter>
-  <filter id="7" type="meshsurface">
+  <filter id="9" type="meshsurface">
     <bins>3</bins>
   </filter>
   <filter id="4" type="mesh">
     <bins>4</bins>
   </filter>
-  <filter id="8" type="meshsurface">
+  <filter id="10" type="meshsurface">
     <bins>4</bins>
   </filter>
+  <filter id="5" type="mesh">
+    <bins>5</bins>
+  </filter>
+  <filter id="11" type="meshsurface">
+    <bins>5</bins>
+  </filter>
+  <filter id="6" type="mesh">
+    <bins>6</bins>
+  </filter>
+  <filter id="12" type="meshsurface">
+    <bins>6</bins>
+  </filter>
   <tally id="1">
     <filters>1</filters>
     <scores>total</scores>
   </tally>
   <tally id="2">
-    <filters>5</filters>
+    <filters>7</filters>
     <scores>current</scores>
   </tally>
   <tally id="3">
@@ -90,7 +112,7 @@
     <scores>total</scores>
   </tally>
   <tally id="4">
-    <filters>6</filters>
+    <filters>8</filters>
     <scores>current</scores>
   </tally>
   <tally id="5">
@@ -98,7 +120,7 @@
     <scores>total</scores>
   </tally>
   <tally id="6">
-    <filters>7</filters>
+    <filters>9</filters>
     <scores>current</scores>
   </tally>
   <tally id="7">
@@ -106,7 +128,23 @@
     <scores>total</scores>
   </tally>
   <tally id="8">
-    <filters>8</filters>
+    <filters>10</filters>
+    <scores>current</scores>
+  </tally>
+  <tally id="9">
+    <filters>5</filters>
+    <scores>total</scores>
+  </tally>
+  <tally id="10">
+    <filters>11</filters>
+    <scores>current</scores>
+  </tally>
+  <tally id="11">
+    <filters>6</filters>
+    <scores>total</scores>
+  </tally>
+  <tally id="12">
+    <filters>12</filters>
     <scores>current</scores>
   </tally>
 </tallies>
diff --git a/tests/regression_tests/filter_mesh/results_true.dat b/tests/regression_tests/filter_mesh/results_true.dat
index 332c8b36c..ec9fe47a3 100644
--- a/tests/regression_tests/filter_mesh/results_true.dat
+++ b/tests/regression_tests/filter_mesh/results_true.dat
@@ -1 +1 @@
-97cf099a24099d2af794752e145841a9ef9f24980c53ee71e3fdd400d4249a7e6f3f52f63132fe2fe8d1973604a72d87910ab13bc3721f7d0bec533b87756847
\ No newline at end of file
+cacc0cedfa243b31f6c44e22bedea400744af14ad139631ec7141c0812ade18e1b53f59e65865ef90d296716a555718cc06108db9c2d434d9d04ec9bb878a81d
\ No newline at end of file
diff --git a/tests/regression_tests/filter_mesh/test.py b/tests/regression_tests/filter_mesh/test.py
index c8aa871a8..eddf0a991 100644
--- a/tests/regression_tests/filter_mesh/test.py
+++ b/tests/regression_tests/filter_mesh/test.py
@@ -51,18 +51,32 @@ def model():
     recti_mesh.y_grid = np.linspace(-7.5, 7.5, 18)
     recti_mesh.z_grid = np.logspace(0, np.log10(7.5), 11)
 
+    cyl_mesh = openmc.CylindricalMesh()
+    cyl_mesh.r_grid = np.linspace(0, 7.5, 18)
+    cyl_mesh.phi_grid = np.linspace(0, 360, 19)
+    cyl_mesh.z_grid = np.linspace(-7.5, 7.5, 17)
+
+    sph_mesh = openmc.SphericalMesh()
+    sph_mesh.r_grid = np.linspace(0, 7.5, 18)
+    sph_mesh.theta_grid = np.linspace(0, 180, 9)
+    sph_mesh.phi_grid = np.linspace(0, 360, 19)
+
     # Create filters
     reg_filters = [
         openmc.MeshFilter(mesh_1d),
         openmc.MeshFilter(mesh_2d),
         openmc.MeshFilter(mesh_3d),
-        openmc.MeshFilter(recti_mesh)
+        openmc.MeshFilter(recti_mesh),
+        openmc.MeshFilter(cyl_mesh),
+        openmc.MeshFilter(sph_mesh)
     ]
     surf_filters = [
         openmc.MeshSurfaceFilter(mesh_1d),
         openmc.MeshSurfaceFilter(mesh_2d),
         openmc.MeshSurfaceFilter(mesh_3d),
-        openmc.MeshSurfaceFilter(recti_mesh)
+        openmc.MeshSurfaceFilter(recti_mesh),
+        openmc.MeshSurfaceFilter(cyl_mesh),
+        openmc.MeshSurfaceFilter(sph_mesh)
     ]
 
     # Create tallies
diff --git a/tests/unit_tests/test_lib.py b/tests/unit_tests/test_lib.py
index ccff33ac3..3572e9863 100644
--- a/tests/unit_tests/test_lib.py
+++ b/tests/unit_tests/test_lib.py
@@ -580,6 +580,68 @@ def test_rectilinear_mesh(lib_init):
     msf = openmc.lib.MeshSurfaceFilter(mesh)
     assert msf.mesh == mesh
 
+def test_cylindrical_mesh(lib_init):
+    deg2rad = lambda deg: deg*np.pi/180
+    mesh = openmc.lib.CylindricalMesh()
+    x_grid = [0., 5., 10.]
+    y_grid = [0., 10., 20.]
+    z_grid = [10., 20., 30.]
+    mesh.set_grid(x_grid, y_grid, z_grid)
+    assert np.all(mesh.lower_left == (0., 0., 10.))
+    assert np.all(mesh.upper_right == (10., deg2rad(20.), 30.))
+    assert np.all(mesh.dimension == (2, 2, 2))
+    for i, diff_x in enumerate(np.diff(x_grid)):
+        for j, diff_y in enumerate(np.diff(y_grid)):
+            for k, diff_z in enumerate(np.diff(z_grid)):
+                assert np.all(mesh.width[i, j, k, :] == (5, deg2rad(10), 10))
+
+    with pytest.raises(exc.AllocationError):
+        mesh2 = openmc.lib.CylindricalMesh(mesh.id)
+
+    meshes = openmc.lib.meshes
+    assert isinstance(meshes, Mapping)
+    assert len(meshes) == 3
+
+    mesh = meshes[mesh.id]
+    assert isinstance(mesh, openmc.lib.CylindricalMesh)
+
+    mf = openmc.lib.MeshFilter(mesh)
+    assert mf.mesh == mesh
+
+    msf = openmc.lib.MeshSurfaceFilter(mesh)
+    assert msf.mesh == mesh
+
+def test_spherical_mesh(lib_init):
+    deg2rad = lambda deg: deg*np.pi/180
+    mesh = openmc.lib.SphericalMesh()
+    x_grid = [0., 5., 10.]
+    y_grid = [0., 10., 20.]
+    z_grid = [10., 20., 30.]
+    mesh.set_grid(x_grid, y_grid, z_grid)
+    assert np.all(mesh.lower_left == (0., 0., deg2rad(10.)))
+    assert np.all(mesh.upper_right == (10., deg2rad(20.), deg2rad(30.)))
+    assert np.all(mesh.dimension == (2, 2, 2))
+    for i, diff_x in enumerate(np.diff(x_grid)):
+        for j, diff_y in enumerate(np.diff(y_grid)):
+            for k, diff_z in enumerate(np.diff(z_grid)):
+                assert np.all(abs(mesh.width[i, j, k, :] - (5, deg2rad(10), deg2rad(10))) < 1e-16)
+
+    with pytest.raises(exc.AllocationError):
+        mesh2 = openmc.lib.SphericalMesh(mesh.id)
+
+    meshes = openmc.lib.meshes
+    assert isinstance(meshes, Mapping)
+    assert len(meshes) == 4
+
+    mesh = meshes[mesh.id]
+    assert isinstance(mesh, openmc.lib.SphericalMesh)
+
+    mf = openmc.lib.MeshFilter(mesh)
+    assert mf.mesh == mesh
+
+    msf = openmc.lib.MeshSurfaceFilter(mesh)
+    assert msf.mesh == mesh
+
 
 def test_restart(lib_init, mpi_intracomm):
     # Finalize and re-init to make internal state consistent with XML.