A vacuum pump housing comprises first (12) and second half-shell stator components (14) defining a plurality of pumping chambers separated by partition members (26, 28, 30, 32). Each pumping chamber comprises an inlet port (42, 44, 46, 48, 50) for receiving fluid and an outlet port (54, 56, 58, 60, 62) through which pumped fluid is exhausted from the chamber. The inlet ports are open on an external surface of the first stator component, and the outlet ports are open on an opposing external surface of the second stator component. The stator components further define transfer channels (66, 68, 70, 72) for conveying fluid between the pumping chambers. Each transfer channel preferably comprises first and second portions located on opposite sides of the housing.