A medical infusion system is described employing a pump for conducting fluid or semi-solids from an upstream portion to a downstream portion of the system. The pump includes upstream and downstream conduit means and a removable cassette communicating between the two. The cassette has a window therein and a diaphragm spans the window. The cassette has inlet and outlet openings valvelessly communicating with the pumping chamber or cavity of the cassette. Fluid in the conduit is pumped by restricting and opening the conduit means at upstream and downstream locations, and displacing the contents of the cassette pumping chamber appropriately.