diff --git a/tests/test_hosvd.py b/tests/test_hosvd.py
index c0038e02..215e6c20 100644
--- a/tests/test_hosvd.py
+++ b/tests/test_hosvd.py
@@ -13,6 +13,15 @@ def sample_tensor():
     return params, tensorInstance
 
 
+@pytest.fixture()
+def sample_tensor_3way():
+    shape = (3, 3, 3)
+    data = np.array(range(1, 28)).reshape(shape, order="F")
+    params = {"data": data, "shape": shape}
+    tensorInstance = ttb.tensor().from_data(data, shape)
+    return params, tensorInstance
+
+
 @pytest.mark.indevelopment
 def test_hosvd_simple_convergence(capsys, sample_tensor):
     (data, T) = sample_tensor
@@ -65,3 +74,48 @@ def test_hosvd_incorrect_dimorder(capsys, sample_tensor):
     dimorder = 1
     with pytest.raises(ValueError):
         _ = ttb.hosvd(T, 1, dimorder=dimorder)
+
+
+@pytest.mark.indevelopment
+def test_hosvd_3way(capsys, sample_tensor_3way):
+    (data, T) = sample_tensor_3way
+    M = ttb.hosvd(T, 1e-4, verbosity=0)
+    capsys.readouterr()
+    print(f"M=\n{M}")
+    core = np.array(
+        [
+            [
+                [-8.301598119750199e01, -5.005881796972034e-03],
+                [-1.268039597172832e-02, 5.842630378620833e00],
+            ],
+            [
+                [3.709974006281391e-02, -1.915213813096568e00],
+                [-5.157111619887230e-01, 5.243776123493664e-01],
+            ],
+        ]
+    )
+    fm0 = np.array(
+        [
+            [-5.452132631706279e-01, -7.321719955012304e-01],
+            [-5.767748638548937e-01, -2.576993904719336e-02],
+            [-6.083364645391598e-01, 6.806321174064961e-01],
+        ]
+    )
+    fm1 = np.array(
+        [
+            [-4.756392343758577e-01, 7.791666394653051e-01],
+            [-5.719678320081717e-01, 7.865197061237804e-02],
+            [-6.682964296404851e-01, -6.218626982406427e-01],
+        ]
+    )
+    fm2 = np.array(
+        [
+            [-1.922305666539489e-01, 8.924016710972924e-01],
+            [-5.140779746206554e-01, 2.627873081852611e-01],
+            [-8.359253825873615e-01, -3.668270547267537e-01],
+        ]
+    )
+    assert np.allclose(M.core.data, core)
+    assert np.allclose(M.u[0], fm0)
+    assert np.allclose(M.u[1], fm1)
+    assert np.allclose(M.u[2], fm2)