A medical pumping system has a supply tube (2), an outlet tube (6), a readily sterilizable, disposable cassette (3) connected to the tubes and engaged with the pump, and means (22,24) such as a motor-driven piston, for intermittently applying pressure to the cassette. The pumping system features a display and switch means (9, 10) on a front panel thereof, a pressure sensor (28), an optical fluid presence sensor (19), and a microprocessor (20) metering the volume of fluid pumped through said cassette (3), monitoring output signals from said sensors (18, 28), controlling the motor-driven piston in accordance with settings entered via said switch means (9,10), and directing output data to said display means (8). The microprocessor has a stored program for performing SET RATE, RUN, HOLD, VOLUME FED, and CLEAR VOLUME functions. The cassette includes 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.