A valve apparatus for medical applications, comprises a flexible member extending across a lumen through which a flow of materials is to be controlled. The flexible member includes a plurality of movable elements formed on opposite sides of a slit extending through the flexible member. The moveable members are biased so that when a pressure less than a predetermined threshold value is applied to the flexible member, the moveable elements are maintained in a closed position in which no flow is permitted past the flexible member and, when a pressure at least as great as the threshold value is applied to the flexible member, the moveable elements are moved to an open position separated from one another along the slit permitting flow through the lumen.
