A pump assembly comprising a housing, a support frame that can be attached to the housing, and a rotor that can rotate within the housing. The housing consists of resilient material and comprises an interior surface, an inlet portion including an inlet for fluid, an outlet portion including an outlet for the fluid, and a diaphragm portion. A housing-engaging surface area of the rotor will form a sealing interference contact with the interior surface, and a chamber-forming surface area of the rotor disposed radially inward from the housing-engaging surface area will form a chamber with the interior surface. When the rotor rotates within the housing as in use, the chamber can convey fluid from the inlet portion to the outlet portion. The diaphragm portion will bear against the chamber-forming surface as the chamber-forming surface travels from the outlet to the inlet, to prevent fluid passing from the outlet to the inlet and to expel the fluid from the chamber through the outlet portion. The support frame will be attached to spaced-apart portions of the housing, and will be sufficiently stiff to counter-balance the torque applied to the housing by the rotor.