A heart valve prosthesis includes a valve member having an inflow end, an outflow end, and a generally cylindrical sidewall portion extending between the inflow end and the outflow end. The valve member includes at least one leaflet moveable relative to the sidewall portion to provide for substantially unidirectional flow of fluid through the valve member. A support of a substantially flexible material positioned is around the sidewall portion. A strip of pliant material is provided around valve member intermediate the inflow end and the outflow end of the valve member in a generally overlying relationship with the support. A covering is provided over a radially outer exposed surface of at least the strip.