diff --git a/pymc/data.py b/pymc/data.py
index cfade3791..c9d8dae3e 100644
--- a/pymc/data.py
+++ b/pymc/data.py
@@ -20,12 +20,14 @@
 from copy import copy
 from typing import Union, cast
 
+import narwhals as nw
 import numpy as np
 import pandas as pd
 import pytensor
 import pytensor.tensor as pt
 import xarray as xr
 
+from narwhals.typing import IntoFrameT, IntoSeriesT
 from pytensor.compile.builders import OpFromGraph
 from pytensor.compile.sharedvalue import SharedVariable
 from pytensor.graph.basic import Variable
@@ -185,7 +187,7 @@ def determine_coords(
     if hasattr(value, "columns"):
         if dims is not None:
             dim_name = dims[1]
-        if dim_name is None and value.columns.name is not None:
+        if dim_name is None and nw.dependencies.is_pandas_dataframe(value) and value.columns.name is not None:
             dim_name = value.columns.name
         if dim_name is not None:
             coords[dim_name] = value.columns
@@ -197,12 +199,12 @@ def determine_coords(
                 # str is applied because dim entries may be None
                 coords[str(dim_name)] = cast(xr.DataArray, value[dim]).to_numpy()
 
-    if isinstance(value, np.ndarray) and dims is not None:
-        if len(dims) != value.ndim:
+    elif (isinstance(value, np.ndarray) or nw.dependencies.is_polars_series(value)) and dims is not None:
+        if len(dims) != len(value.shape):  # Polars objects have no .ndim ...
             raise ShapeError(
                 "Invalid data shape. The rank of the dataset must match the length of `dims`.",
                 actual=value.shape,
-                expected=value.ndim,
+                expected=len(value.shape),
             )
         for size, dim in zip(value.shape, dims):
             coord = model.coords.get(dim, None)
@@ -219,7 +221,7 @@ def determine_coords(
 
 def Data(
     name: str,
-    value,
+    value: IntoFrameT | IntoSeriesT | xr.DataArray | np.ndarray,
     *,
     dims: Sequence[str] | None = None,
     coords: dict[str, Sequence | np.ndarray] | None = None,
@@ -248,7 +250,7 @@ def Data(
     ----------
     name : str
         The name for this variable.
-    value : array_like or pandas.Series, pandas.Dataframe
+    value : array_like or Narwhals-compatible Series or DataFrame
         A value to associate with this variable.
     dims : str, tuple of str or tuple of None, optional
         Dimension names of the random variables (as opposed to the shapes of these