diff --git a/test/blockstructured/poisson/CMakeLists.txt b/test/blockstructured/poisson/CMakeLists.txt
index 7ce13eff78142fb61a2ea43c5c7cb45c388a0bc6..1b48ca5f343efeffe528a5066d3bc4073898b8a5 100644
--- a/test/blockstructured/poisson/CMakeLists.txt
+++ b/test/blockstructured/poisson/CMakeLists.txt
@@ -1,7 +1,7 @@
 add_subdirectory(3d)
 
 
-dune_symlink_to_source_files(FILES square.msh)
+dune_symlink_to_source_files(FILES square.msh cube.msh)
 
 dune_add_formcompiler_system_test(UFLFILE poisson.ufl
         BASENAME blockstructured_poisson
diff --git a/test/blockstructured/poisson/cube.msh b/test/blockstructured/poisson/cube.msh
new file mode 100644
index 0000000000000000000000000000000000000000..0eac3436f979911323a1307eb10e1a0686f5b4a1
--- /dev/null
+++ b/test/blockstructured/poisson/cube.msh
@@ -0,0 +1,615 @@
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+198 5 0 103 108 223 330 104 109 226 332
+199 5 0 104 109 226 332 105 110 229 334
+200 5 0 106 210 184 111 105 334 229 110
+201 5 0 16 50 36 13 112 117 316 265
+202 5 0 112 117 316 265 113 118 318 268
+203 5 0 113 118 318 268 114 119 320 271
+204 5 0 114 119 320 271 115 120 322 274
+205 5 0 116 193 206 121 115 274 322 120
+206 5 0 24 45 44 25 82 87 347 283
+207 5 0 82 87 347 283 83 88 348 284
+208 5 0 83 88 348 284 84 89 349 285
+209 5 0 84 89 349 285 85 90 350 286
+210 5 0 86 198 214 91 85 286 350 90
+211 5 0 21 51 34 22 172 177 308 275
+212 5 0 172 177 308 275 173 178 310 277
+213 5 0 173 178 310 277 174 179 312 279
+214 5 0 174 179 312 279 175 180 314 281
+215 5 0 176 197 204 181 175 281 314 180
+216 5 0 56 8 7 18 359 232 231 142
+217 5 0 359 232 231 142 361 236 235 143
+218 5 0 361 236 235 143 363 240 239 144
+219 5 0 363 240 239 144 365 244 243 145
+220 5 0 218 146 187 188 365 145 243 244
+221 5 0 33 32 3 2 296 295 219 221
+222 5 0 296 295 219 221 299 298 222 224
+223 5 0 299 298 222 224 302 301 225 227
+224 5 0 302 301 225 227 305 304 228 230
+225 5 0 203 182 183 202 305 230 228 304
+226 5 0 5 43 26 6 233 343 287 234
+227 5 0 233 343 287 234 237 344 288 238
+228 5 0 237 344 288 238 241 345 289 242
+229 5 0 241 345 289 242 245 346 290 246
+230 5 0 185 186 199 213 245 246 290 346
+231 5 0 55 54 57 60 157 360 147 152
+232 5 0 157 360 147 152 158 362 148 153
+233 5 0 158 362 148 153 159 364 149 154
+234 5 0 159 364 149 154 160 366 150 155
+235 5 0 161 156 151 217 160 155 150 366
+236 5 0 52 39 45 61 97 327 87 92
+237 5 0 97 327 87 92 98 329 88 93
+238 5 0 98 329 88 93 99 331 89 94
+239 5 0 99 331 89 94 100 333 90 95
+240 5 0 101 96 91 209 100 95 90 333
+$EndElements
diff --git a/test/blockstructured/poisson/poisson_tensor.mini b/test/blockstructured/poisson/poisson_tensor.mini
index 9eb55a9a1fdafcfc2e862d51b08365700e552b28..c2922469f5d631d8647edbee40f04133b5908b8d 100644
--- a/test/blockstructured/poisson/poisson_tensor.mini
+++ b/test/blockstructured/poisson/poisson_tensor.mini
@@ -1,8 +1,16 @@
 __name = blockstructured_poisson_tensor_{__exec_suffix}
-__exec_suffix = nonvec, vec | expand vectorized
+__exec_suffix = {grid_suffix}_{vec_suffix}_{dim_suffix}
 
-cells = 10 10
-extension = 1. 1.
+dim = 2, 3 | expand dimension
+
+grid_suffix = structured, unstructured | expand unstructured
+vec_suffix = nonvec, vec | expand vectorized
+dim_suffix = 2d, 3d | expand dimension
+
+cells = 10, 5 | expand dimension | repeat {dim}
+extension = 1. | repeat {dim}
+
+gmshFile = square.msh, cube.msh | expand dimension
 
 [wrapper.vtkcompare]
 name = {__name}
@@ -11,10 +19,15 @@ extension = vtu
 
 [formcompiler]
 compare_l2errorsquared = 1e-7
+grid_unstructured = 0, 1 | expand unstructured
 
 [formcompiler.r]
 matrix_free = 1
 vectorization_blockstructured = 0, 1 | expand vectorized
 generate_jacobians = 0
 blockstructured = 1
-number_of_blocks = 8
+number_of_blocks = 8, 4 | expand dimension
+
+[formcompiler.ufl_variants]
+cell = quadrilateral, hexahedron | expand dimension
+dim = 2, 3 | expand dimension
\ No newline at end of file
diff --git a/test/blockstructured/poisson/poisson_tensor.ufl b/test/blockstructured/poisson/poisson_tensor.ufl
index 239e14fca9550031cd53994d9528cb0c41e424a6..568e697ee377fa93b3a31468d4af3009daf7366b 100644
--- a/test/blockstructured/poisson/poisson_tensor.ufl
+++ b/test/blockstructured/poisson/poisson_tensor.ufl
@@ -1,12 +1,10 @@
-cell = quadrilateral
-
 x = SpatialCoordinate(cell)
 
-I = Identity(2)
-A = as_matrix([[x[i]*x[j] + I[i,j] for j in range(2)] for i in range(2)])
-g = x[0]**2 + x[1]**2
-c = 8.
-f = -4.
+I = Identity(dim)
+A = as_matrix([[x[i]*x[j] + I[i,j] for j in range(dim)] for i in range(dim)])
+g = sum([c**2 for c in x])
+c = 6. + (dim - 1) * 2
+f = - 2. * dim
 
 V = FiniteElement("CG", cell, 1)
 u = TrialFunction(V)
diff --git a/test/blockstructured/poisson/square.geo b/test/blockstructured/poisson/square.geo
new file mode 100644
index 0000000000000000000000000000000000000000..8a630d3011a5c0ff219a141d546086af864f3655
--- /dev/null
+++ b/test/blockstructured/poisson/square.geo
@@ -0,0 +1,28 @@
+// Gmsh project created on Tue Oct 23 11:21:07 2018
+SetFactory("OpenCASCADE");
+//+
+Point(1) = {0, 0, 0, 0.23};
+//+
+Point(2) = {0, 1, 0, 0.23};
+//+
+Point(3) = {1, 1, 0, 0.23};
+//+
+Point(4) = {1, 0, 0, 0.23};
+//+
+Line(1) = {1, 4};
+//+
+Line(2) = {4, 3};
+//+
+Line(3) = {3, 2};
+//+
+Line(4) = {2, 1};
+//+
+Line Loop(1) = {3, 4, 1, 2};
+//+
+Plane Surface(1) = {1};
+//+
+Recombine Surface {1};
+//+
+Extrude {0, 0, 1} {
+  Surface{1}; Layers{5}; Recombine;
+}