A pump system for an infusion system includes a linear drive (36, 36′) which minimizes the space occupied by the pump components in a portable housing (10, 10′). A motor (34) and a motor drive shaft (42) are arranged in parallel with, and adjacent to a syringe (14, 14′) and lead screw (94, 94′). A gear box (54) connects the drive shaft and lead screw to transfer rotational movements between them. A piston driving member, such as a cone (116) or drive nut (116′) converts the rotational movement of the lead screw into linear motion of a syringe piston (24). Sensors (150, 152) detect when the piston or cone is in a “home” position and in an “end” position, respectively. Optionally, a proximity sensor (170) is used to ensure that the cone and the piston (24) are abutting during dispensing. Alternatively, a clamping member (350) selectively clamps the lead screw (94′) against linear motion in at least a dispensing direction.