A vane pump has a casing, a rotor rotatably mounted in the casing, and a plurality of vanes mounted in the rotor and projecting variable amounts from an outer peripheral wall of the rotor. The outer peripheral wall of the rotor and an inner peripheral wall of the casing are shaped cylindrical. The rotor has an axis of rotation offset from the center of the inner peripheral wall of the casing. Stationary cams concentric with the inner wall of the casing act on proximal ends of the vanes, so that distal ends of the vanes revolve in close vicinity of but not in pressure contact with the inner wall of the casing.