A venous valve prosthesis includes a hollow conduit (40) defining a central passageway through which blood may flow. Opposing, pliable leaflet members (30) are located within the conduit and move back and forth between a first, open position, whereby blood may flow through the central passageway in a first direction, and a second, closed position, whereby blood is prevented from backflowing through the central passageway in a second direction which is opposite the first direction. A hollow and generally cylindrical support member (10, 20) retains the leaflet members and is coaxially disposed within the conduit. The support member includes opposing cutaway regions (18) defining two axially extending struts (16) supporting the leaflet members. The cutaway regions, in cooperation with the struts, allow the leaflet members to collapse inwardly to the closed position.