A pump apparatus for an electrohydraulic power steering mechanism for a vehicle includes a hydraulic pump, a working line, a pressure generator, a first control line, a preliminary pressure line, a compensation tank, a shut-off valve having a control inlet, and a second control line. The hydraulic pump is designed to pump a hydraulic oil out of a pump chamber to a pump outlet of the hydraulic pump. The pressure generator has a pressure generation inlet and a pressure generation outlet, and the pressure generator is designed to generate, using an inlet pressure present at the pressure generation inlet, an outlet pressure which can be provided at the pressure generation outlet and is lower than the inlet pressure. As a result, a preliminary pressure can be generated in the pump chamber.