A multi-stage vacuum pump of the dry pump type is disclosed. The multi-stage vacuum pump includes a plurality of pumping stages each respectively having an inlet and an outlet, the pumping stages being mounted in series between a suction port and a discharge port of the vacuum pump, characterized in that the vacuum pump also includes at least one valve configured to dump pressure from a pumping stage, said valve being arranged in the upper part of the vacuum pump, on the same side as the inlet of the pumping stage.