diff --git a/RELEASE-NOTES.md b/RELEASE-NOTES.md
index da62607513..6d58c0adca 100644
--- a/RELEASE-NOTES.md
+++ b/RELEASE-NOTES.md
@@ -88,6 +88,7 @@ This includes API changes we did not warn about since at least `3.11.0` (2021-01
 - New features for BART:
   -  Added linear response, increased number of trees fitted per step [5044](https://github.com/pymc-devs/pymc3/pull/5044).
   -  Added partial dependence plots and individual conditional expectation plots [5091](https://github.com/pymc-devs/pymc3/pull/5091).
+- `pm.Data` now passes additional kwargs to `aesara.shared`. [#5098](https://github.com/pymc-devs/pymc/pull/5098)
 - ...
 
 
diff --git a/pymc/data.py b/pymc/data.py
index 649d59828c..804595831b 100644
--- a/pymc/data.py
+++ b/pymc/data.py
@@ -464,8 +464,8 @@ def align_minibatches(batches=None):
 
 
 class Data:
-    """Data container class that wraps the Aesara ``SharedVariable`` class
-    and lets the model be aware of its inputs and outputs.
+    """Data container class that wraps :func:`aesara.shared` and lets
+    the model be aware of its inputs and outputs.
 
     Parameters
     ----------
@@ -478,10 +478,12 @@ class Data:
         random variables). Use this when `value` is a pandas Series or DataFrame. The
         `dims` will then be the name of the Series / DataFrame's columns. See ArviZ
         documentation for more information about dimensions and coordinates:
-        https://arviz-devs.github.io/arviz/notebooks/Introduction.html
+        :ref:`arviz:quickstart`.
     export_index_as_coords: bool, optional, default=False
         If True, the `Data` container will try to infer what the coordinates should be
         if there is an index in `value`.
+    **kwargs: dict, optional
+        Extra arguments passed to :func:`aesara.shared`.
 
     Examples
     --------
@@ -512,7 +514,15 @@ class Data:
     https://docs.pymc.io/notebooks/data_container.html
     """
 
-    def __new__(self, name, value, *, dims=None, export_index_as_coords=False):
+    def __new__(
+        self,
+        name,
+        value,
+        *,
+        dims=None,
+        export_index_as_coords=False,
+        **kwargs,
+    ):
         if isinstance(value, list):
             value = np.array(value)
 
@@ -528,7 +538,7 @@ def __new__(self, name, value, *, dims=None, export_index_as_coords=False):
 
         # `pandas_to_array` takes care of parameter `value` and
         # transforms it to something digestible for pymc
-        shared_object = aesara.shared(pandas_to_array(value), name)
+        shared_object = aesara.shared(pandas_to_array(value), name, **kwargs)
 
         if isinstance(dims, str):
             dims = (dims,)
diff --git a/pymc/tests/test_data_container.py b/pymc/tests/test_data_container.py
index cfbdaa32a9..1abc6c0329 100644
--- a/pymc/tests/test_data_container.py
+++ b/pymc/tests/test_data_container.py
@@ -366,6 +366,19 @@ def test_implicit_coords_dataframe(self):
         assert "columns" in pmodel.coords
         assert pmodel.RV_dims == {"observations": ("rows", "columns")}
 
+    def test_data_kwargs(self):
+        strict_value = True
+        allow_downcast_value = False
+        with pm.Model():
+            data = pm.Data(
+                "data",
+                value=[[1.0], [2.0], [3.0]],
+                strict=strict_value,
+                allow_downcast=allow_downcast_value,
+            )
+        assert data.container.strict is strict_value
+        assert data.container.allow_downcast is allow_downcast_value
+
 
 def test_data_naming():
     """