Medical stents having valves and their methods of manufacture are disclosed. The valve may be basket-shaped and formed integral to a medical stent to prevent undesirable backflow across the valve. The valve can be formed by converting the braided wires of the stent, by providing elastomeric material onto a mold or fixture to form an elastomeric valve, or by attaching a gasket valve. The valve is normally closed but configured to allow easy opening in response to a predetermined condition.