To increase precision of flow in multiple channels of a peristaltic pump, a plurality of spring biased cassettes are mounted to cooperate with a spool having a plurality of elongated rollers which orbit about its center so that each elongated roller in succession compresses a plurality of flexible tubes in the channels against corresponding cam surfaces in the cassettes, spaced from the rollers by surfaces of the cassettes which are in contact with the rolles. In each cassette, the cam is mounted between side plates against which the rollers roll, which are spring biased against the rollers and hinged at a center location to provide precision determined only by the precision of the cam to side plate edge dimension. The cam is shaped to reduce pulses during roller lift-off from the cam surface to provide for pulse-free flow.