A multi-stage vacuum pump comprising: first and second half-shell stator components defining a plurality of pumping chambers and for assembly together along respective longitudinally extending faces; first and second end stator components for assembly at respective longitudinal end faces of the first and second half-shell stator components; gaskets for sealing between the first and second half-shell stator components when assembled together at the longitudinally extending faces; and O-rings for sealing between the first and second end stator components and the first and second half-shell stator components when assembled; wherein annular channels intersect longitudinal recesses and each longitudinal recess comprises a stop fixed relative to the intersection, and the gasket and the longitudinal recess are configured that when the gasket is located in the recess during assembly the gasket is biased against the stop for locating an end portion of the gasket relative to the intersection.