A linear peristaltic pump of the type for removable engagement of a portion of a flexible tubing and having a plurality of sequentially actuated pumping elements which act along the engaged portion of the flexible tubing, with the pumping elements reciprocated in a first direction to collapse adjacent segments of the tubing and then in a second direction to release the adjacent segments of the tubing, each pumping element having a flat pumping surface reciprocated in a sequence so that fluid in the flexible tubing is moved along the engaged portion of the tubing. The linear peristaltic pump is provided with a plurality of opposed pairs of pivotable reshaping fingers, with each pair of the reshaping fingers interposed adjacent to one of the pumping elements in sequence along the engaged portion of the flexible tubing. A finger drive and follower mechanism is formed by and engaged between each of the plurality of pairs of reshaping fingers and the adjacent ones of the pumping elements for actuating the reshaping fingers into reshaping engagement with the flexible tubing upon release thereof by the adjacent one of the pumping elements.