diff --git a/src/highdicom/spatial.py b/src/highdicom/spatial.py
index 54a64925..d5fab854 100644
--- a/src/highdicom/spatial.py
+++ b/src/highdicom/spatial.py
@@ -917,3 +917,45 @@ def map_coordinate_into_pixel_matrix(
         round(pixel_matrix_coordinates[1]),
         round(pixel_matrix_coordinates[2]),
     )
+
+
+def are_points_coplanar(
+    points: np.ndarray,
+    tol: float = 1e-5,
+) -> bool:
+    """Check whether a set of 3D points are coplanar (to within a tolerance).
+
+    Parameters
+    ----------
+    points: np.ndarray
+        Numpy array of shape (n x 3) containing 3D points.
+    tol: float
+        Tolerance on the distance of the furthest point from the plane of best
+        fit.
+
+    Returns
+    -------
+    bool:
+        True if the points are coplanar within a tolerance tol, False
+        otherwise. Note that if n < 4, points are always coplanar.
+
+    """
+    if points.ndim != 2 or points.shape[1] != 3:
+        raise ValueError("Array should have shape (n x 3).")
+
+    n = points.shape[0]
+    if n < 4:
+        # Any set of three or fewer points is coplanar
+        return True
+
+    # Center points by subtracting mean
+    c = np.mean(points, axis=0, keepdims=True)
+    points_centered = points - c
+
+    # Use a SVD to determine the normal of the plane of best fit, then
+    # find maximum deviation from it
+    u, _, _ = np.linalg.svd(points_centered.T)
+    normal = u[:, -1]
+    deviations = normal.T @ points_centered.T
+    max_dev = np.abs(deviations).max()
+    return max_dev <= tol
diff --git a/src/highdicom/sr/value_types.py b/src/highdicom/sr/value_types.py
index 5969ffe4..25ea70a5 100644
--- a/src/highdicom/sr/value_types.py
+++ b/src/highdicom/sr/value_types.py
@@ -23,6 +23,7 @@
 from pydicom.sr.coding import Code
 from pydicom.valuerep import DA, DS, TM, DT, PersonName
 
+from highdicom.spatial import are_points_coplanar
 from highdicom.sr.coding import CodedConcept
 from highdicom.sr.enum import (
     GraphicTypeValues,
@@ -1763,6 +1764,25 @@ def __init__(
                     '(x, y, z) triplets in three-dimensional patient or '
                     'slide coordinate space.'
                 )
+            if graphic_type == GraphicTypeValues3D.POLYGON:
+                if not np.array_equal(graphic_data[0], graphic_data[-1]):
+                    raise ValueError(
+                        'Graphic data of a 3D scoord of graphic type "POLYGON" '
+                        'must be closed, i.e. the first and last points must '
+                        'be equal.'
+                    )
+
+        # Check for coplanarity, if required by the graphic type
+        if graphic_type in (
+            GraphicTypeValues3D.POLYGON,
+            GraphicTypeValues3D.ELLIPSE,
+        ):
+            if not are_points_coplanar(graphic_data):
+                raise ValueError(
+                    'Graphic data of a 3D scoord of type '
+                    f'"{graphic_type.value}" must contain co-planar points.'
+                )
+
         # Flatten list of coordinate triplets
         self.GraphicData = graphic_data.flatten().tolist()
         self.ReferencedFrameOfReferenceUID = frame_of_reference_uid
diff --git a/tests/test_sr.py b/tests/test_sr.py
index d4b94aaf..280bf323 100644
--- a/tests/test_sr.py
+++ b/tests/test_sr.py
@@ -1168,6 +1168,38 @@ def test_scoord3d_item_construction_polygon(self):
         with pytest.raises(AttributeError):
             i.FiducialUID
 
+    def test_scoord3d_item_construction_non_closed_polygon(self):
+        name = codes.DCM.ImageRegion
+        graphic_type = GraphicTypeValues3D.POLYGON
+        graphic_data = np.array([
+            [1.0, 1.0, 1.0], [2.0, 2.0, 1.0], [1.0, 2.0, 1.0]  # non-closed
+        ])
+        frame_of_reference_uid = '1.2.3'
+        with pytest.raises(ValueError):
+            Scoord3DContentItem(
+                name=name,
+                graphic_type=graphic_type,
+                graphic_data=graphic_data,
+                frame_of_reference_uid=frame_of_reference_uid,
+                relationship_type=RelationshipTypeValues.INFERRED_FROM
+            )
+
+    def test_scoord3d_item_construction_non_coplanar_polygon(self):
+        name = codes.DCM.ImageRegion
+        graphic_type = GraphicTypeValues3D.POLYGON
+        graphic_data = np.array([
+            [1.0, 1.0, 1.0], [2.0, 2.0, 1.0], [1.0, 1.0, 3.0]  # non-coplanr
+        ])
+        frame_of_reference_uid = '1.2.3'
+        with pytest.raises(ValueError):
+            Scoord3DContentItem(
+                name=name,
+                graphic_type=graphic_type,
+                graphic_data=graphic_data,
+                frame_of_reference_uid=frame_of_reference_uid,
+                relationship_type=RelationshipTypeValues.INFERRED_FROM
+            )
+
     def test_container_item_from_dataset(self):
         code_name_ds = _build_coded_concept_dataset(codes.DCM.Finding)
         code_value_ds = _build_coded_concept_dataset(codes.SCT.Neoplasm)