A pump device, in particular for a brake system of a motor vehicle, includes two hydraulic chambers, a linear drive, and a pump piston. Each of the chambers has at least two fluid connections. The pump piston interacts with the chambers. The linear drive is embodied as a reluctance drive and includes a longitudinally movable armature, a housing-fastened stator that is configured to receive current, and at least one spring element. The at least one spring element is associated with the armature, and is configured to counteract a drive force of the reluctance drive. The armature is connected to the pump piston.