Abstract: A progressive cavity pump or motor, particularly suitable for hydrocarbon recovery operations, includes a rotor 20 and a stator 10. Fluid pressure in cavities between the stator and the rotor create torque which rotates the bit. An interior surface of the stator is rigidly secured to the outer housing of the pump stator and defines an interior profile. A substantially uniform thickness elastomeric layer 62 is supported on the outer housing. The pump rotor has an exterior profile which corresponds with the interior profile of the elastomeric layer.