An infusion pump for delivery of drugs to a patient includes a unit in which the pump mechanism is situated and a cassette through which the drugs to be delivered to the patient are pumped. The cassette includes a path for the fluid to flow from a drug vial to an outlet port. Disposed along the path are recesses for an inlet valve, a pressurization region, and an outlet valve. The cassette is sealed by an elastomeric layer to maintain the drugs to be delivered in a contaminant-free condition. The pump includes an inlet valve which has a contour matching the recess of the inlet port, and an outlet valve matching the recess of the outlet port. By biasing the inlet and outlet valves against the recesses, a pumping chamber is created. A piston in the unit pressurizes the pumping chamber to open the outlet valve and permit fluid to escape. By appropriate timing of the operation of the inlet valve and the piston, a continuous stream of fluid is delivered by the pump to the patient.