diff --git a/.github/workflows/pytest.yml b/.github/workflows/pytest.yml
index 3a382d5..6081f94 100644
--- a/.github/workflows/pytest.yml
+++ b/.github/workflows/pytest.yml
@@ -16,7 +16,7 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        python-version: ["3.8", "3.9", "3.10"]
+        python-version: ["3.8", "3.9", "3.10", "3.11", "3.12"]
 
     steps:
     - uses: actions/checkout@v3
diff --git a/pyfive/dataobjects.py b/pyfive/dataobjects.py
index a2fe60b..0730e12 100644
--- a/pyfive/dataobjects.py
+++ b/pyfive/dataobjects.py
@@ -20,6 +20,9 @@
 from .misc_low_level import Heap, SymbolTable, GlobalHeap, FractalHeap
 from .indexing import OrthogonalIndexer, ZarrArrayStub
 
+# these constants happen to have the same value...
+UNLIMITED_SIZE = UNDEFINED_ADDRESS
+
 
 class DataObjects(object):
     """
@@ -182,7 +185,7 @@ def unpack_attribute(self, offset):
         offset += _padded_size(attr_dict['datatype_size'], padding_multiple)
 
         # read in the dataspace information
-        shape = determine_data_shape(self.msg_data, offset)
+        shape, maxshape = determine_data_shape(self.msg_data, offset)
         items = int(np.product(shape))
         offset += _padded_size(attr_dict['dataspace_size'], padding_multiple)
 
@@ -248,7 +251,16 @@ def shape(self):
         """ Shape of the dataset. """
         msg = self.find_msg_type(DATASPACE_MSG_TYPE)[0]
         msg_offset = msg['offset_to_message']
-        return determine_data_shape(self.msg_data, msg_offset)
+        shape, maxshape = determine_data_shape(self.msg_data, msg_offset)
+        return shape
+
+    @property
+    def maxshape(self):
+        """ Maximum Shape of the dataset. (None for unlimited dimension) """
+        msg = self.find_msg_type(DATASPACE_MSG_TYPE)[0]
+        msg_offset = msg['offset_to_message']
+        shape, maxshape = determine_data_shape(self.msg_data, msg_offset)
+        return maxshape
 
     @property
     def fillvalue(self):
@@ -779,9 +791,15 @@ def determine_data_shape(buf, offset):
 
     ndims = header['dimensionality']
     dim_sizes = struct.unpack_from('<' + 'Q' * ndims, buf, offset)
+    offset += 8 * ndims
     # Dimension maximum size follows if header['flags'] bit 0 set
+    if header['flags'] & 2**0:
+        maxshape = struct.unpack_from('<' + 'Q' * ndims, buf, offset)
+        maxshape = tuple((None if d == UNLIMITED_SIZE else d) for d in maxshape)
+    else:
+        maxshape = dim_sizes
     # Permutation index follows if header['flags'] bit 1 set
-    return dim_sizes
+    return dim_sizes, maxshape
 
 
 # HDF5 Structures
diff --git a/pyfive/high_level.py b/pyfive/high_level.py
index e13bdc9..6614f3a 100644
--- a/pyfive/high_level.py
+++ b/pyfive/high_level.py
@@ -310,6 +310,11 @@ def shape(self):
         """ shape attribute. """
         return self._dataobjects.shape
 
+    @property
+    def maxshape(self):
+        """ maxshape attribute. (None for unlimited dimensions) """
+        return self._dataobjects.maxshape
+
     @property
     def ndim(self):
         """ number of dimensions. """