Abstract: Rotary vane pumps include casings having asymmetrical cavities that accommodate a rotor. For a single pump chamber, one portion of the rotor abuts or nearly abuts the inner wall of the cavity at a single location while one portion of the rotor and the inner wall are not in contact with each other thereby defining a pump chamber. For a dual pump chamber embodiment, two diametrically opposed portions of the rotor abut or nearly abut the inner wall of the cavity while two portions of the rotor and inner wall are not in contact with each other thereby defining the two pump chambers. The two pump chambers are disposed on opposite sides of the minor axis of the cavity. The cavities of each pump are skewed so each pump chamber is larger in volume at the inlet end than at the outlet end.