Peristaltic pumps are made up of a series of parallel fingers driven in a vertical reciprocating movement. Each finger's movement is offset with respect to the preceding one in such a way that the ends of the fingers form a sine wave that moves in the direction of pumping. The ends of the fingers press down on a flexible tube placed between the fingers and a platen. The finger furthest down causes an occlusion, which migrates in the downstream direction of the pump from one finger to the next, ending with the last. When the last finger is in the occluding position, the first finger at least is once again in the occluding position, thereby causing the fluid in the tube to move.