Abstract: A well pump includes a piston and an inlet and/or outlet valve assembly of special structure. Each is formed of a body of organic polymer, preferably PTFE. Each includes a cavity in its upper portion and at least one passage leading from the cavity to the bottom of the block. A screen covers each cavity and a valve disk covers each screen. Flexible sealing flanges extend upwardly and downwardly from the periphery of the piston block. The outlet valve block has a sliding block and sealing fit with the piston rod.