diff --git a/devito/operator/operator.py b/devito/operator/operator.py
index 58fab20495..c0bb6145a6 100644
--- a/devito/operator/operator.py
+++ b/devito/operator/operator.py
@@ -1396,15 +1396,21 @@ def _physical_deviceid(self):
             visible_device_var, visible_devices = get_visible_devices()
             if visible_devices is None:
                 return logical_deviceid
+            elif len(visible_devices) == 1:
+                # Only one visible device, it's clearly the one we want
+                return visible_devices[0]
+            elif logical_deviceid <= len(visible_devices):
+                # Map the logical device ID to the physical one
+                return visible_devices[logical_deviceid]
             else:
-                try:
-                    return visible_devices[logical_deviceid]
-                except IndexError as e:
-                    errmsg = (f"A deviceid value of {logical_deviceid} is not valid "
-                              f"with {visible_device_var}={visible_devices}. Note that "
-                              "deviceid corresponds to the logical index within the "
-                              "visible devices, not the physical device index.")
-                    raise ValueError(errmsg) from e
+                # Logical device ID is out of bounds, likely from oversubscription
+                # Print a warning and map modulo the number of visible devices
+                deviceid = visible_devices[logical_deviceid % len(visible_devices)]
+                warning(f"Logical device ID {logical_deviceid} is out of bounds "
+                        f"for {len(visible_devices)} visible devices"
+                        f" in {visible_device_var}."
+                        f"Mapping to device ID {deviceid} instead.")
+                return visible_devices[logical_deviceid % len(visible_devices)]
         else:
             return None
 
diff --git a/tests/test_gpu_common.py b/tests/test_gpu_common.py
index a639c5bbe6..e84d0df5d8 100644
--- a/tests/test_gpu_common.py
+++ b/tests/test_gpu_common.py
@@ -108,7 +108,13 @@ def test_visible_devices(self, env_variables):
         assert argmap2._physical_deviceid == 0
 
     @pytest.mark.parallel(mode=2)
-    @pytest.mark.parametrize('visible_devices', ["1,2", "1,0", "0,2,3"])
+    @pytest.mark.parametrize('visible_devices', [
+        "1,2", "1,0", "0,2,3",
+        # Per rank VISIBLE_DEVICE
+        ("1", "0"),
+        # Oversubscribed
+        "1",
+    ])
     def test_visible_devices_mpi(self, visible_devices, mode):
         """
         Test that physical device IDs used for querying memory on a device via
@@ -122,11 +128,18 @@ def test_visible_devices_mpi(self, visible_devices, mode):
 
         eq = Eq(u, u+1)
 
-        with switchenv({'CUDA_VISIBLE_DEVICES': visible_devices}):
+        if isinstance(visible_devices, tuple):
+            cu_device = visible_devices[rank]
+            expected = int(cu_device)
+        else:
+            cu_device = visible_devices
+            devices = visible_devices.split(',')
+            expected = int(devices[rank % len(devices)])
+
+        with switchenv({'CUDA_VISIBLE_DEVICES': cu_device}):
             op1 = Operator(eq)
             argmap1 = op1.arguments()
-            devices = [int(i) for i in visible_devices.split(',')]
-            assert argmap1._physical_deviceid == devices[rank]
+            assert argmap1._physical_deviceid == expected
 
         # In default case, physical deviceid will equal rank
         op2 = Operator(eq)