A replacement heart valve comprising a memory shape element. The various embodiments use internal body heat to seat and retain the valve within a blood passage. The element can be provided in a variety of shapes and sizes, and is at least partially encased within an inert and pliant encasing material. The encasing material is one that is adapted to be contiguous with the structure of the valve nozzle or backflow-resistant leaf structure, and may be used in combination with existing stents or an incorporated stent, including ones having a structure similar to conventional stents.
