A pumping finger subassembly for a peristaltic infusion pump has a housing, a pinch member, a block member, and at least one biasing spring. The housing includes a transverse slot, a first side wall, and an open second side through which the pinch member and biasing spring(s) are inserted into the transverse slot. The block member includes a foot portion and a side wall portion. The foot portion is insertable into the housing through the open second side such that the block member is constrained against movement relative to the housing and the side wall portion of the block member opposes the first side wall of the housing, whereby the pinch member is supported on both lateral sides to prevent tilting of the pinch member.