A self-cleaning screen for shallow water pumping includes a rotatable drum made of mesh material for removing debris from water passing into the drum, and a suction chamber within the drum for feeding water to a suction pipe connected to a centrifugal pump. Inlet openings are arranged across a bottom side of the suction chamber. A check valve assembly is provided to prevent water from back flowing through the inlet openings, to thereby maintain a prime in the suction pipe when the pump is off. The check valve assembly includes valve members that are slidably mounted above the inlet openings for movement between closed and open positions. The valve members move upwardly from their closed positions to their open positions upon movement of water through the inlet openings into the suction chamber, and return to their closed positions by force of gravity when water stops flowing into the suction chamber.