A pump assembly for generating pressure in a brake circuit of a controllable power brake system of a motor vehicle. The pump assembly has, as a pressure generator, a piston-cylinder unit in which a piston is actuated with the aid of a piston drive. The piston drive converts a rotational movement, with which a nut of this piston drive is driven, into a translatory movement of a spindle, which is in turn connected to the piston in a rotationally fixed manner. The piston is a steel component in which a plastic deformation at a piston head forms a device for connecting the spindle to the piston in a rotationally fixed manner.