A readily sterilizable, disposable cassette (3) can be used in a medical pumping system having a supply tube (2), an outlet tube (6) and means (22,24), such as a motor-driven piston, for intermittently applying pressure to the cassette. The cassette features a hydraulically self-actuating inlet valve (44) communicating with the supply tube (2), a hydraulically self-actuating outlet check valve (42) communicating with, and preventing backflow from, the outlet tube (6), a hollow, resilient compressible member, such as a bellows (34), having an interior communicating with the inlet and outlet valves, and a support structure (30,36,38) securing together the tubes, valves and bellows in operating relation. Preferably, the inlet and outlet valves are a unitary element. An optical sensing system detects fluid exhaustion in the cassette. The cassette has an irregularly-shaped cap (38) which prevents incorrect insertion into a pump.