The invention relates to a pump device (1), in particular for a brake system (2) of a motor vehicle, comprising a linear drive (4), which is designed as a reluctance drive and, for this purpose, has alongitudinally movable armature (8) and a housing-fastened stator (6) that can be supplied with current, wherein at least one spring element (13), which counteracts a drive force of the reluctance drive, is associated with the armature (8), and wherein the armature (8) is connected to a pump piston (5). According to the invention, the pump device (1) has two hydraulic chambers (16, 17), each of which has at least two fluid connections (20-23) and with which the pump piston (5) interacts.