A rotary reciprocating pump comprises: i) a pump housing having intake and discharge ports; a shaft driven rotary piston carder, rotatably carrying pistons circularly arranged therearound; ii) a driven rotary cylinder block having a plurality of cylinder bores therein, circularly arranged therearound for reception of the pistons, and having a flat outer side portion having an intake/discharge port therethrough communicating with the cylinder bores; iii) a stationary sloping inner control surface portion in sliding proximity with the outer side portion of the rotating cylinder block, the control surface portion configured so that the cylinder block moves outwardly for intake and inwardly for discharge, the control surface portion also having grooved openings therethrough to appropriately communicate with the ports to the bore through the cylinder block and with the intake and discharge ports in the pump housing; and, iv) a spring biasing the cylinder blocks towards the control surface portion.