Abstract: A pump jack assembly has a horsehead mounted to rock on a frame; a polished rod connected to the horsehead; and a hydraulic motor connected to rock the horsehead. The pump jack assembly may have a crank assembly connected between the hydraulic motor and the horsehead, the crank assembly having one or more counterweights; a hydraulic pump; a fluid supply line and a fluid return line between the hydraulic pump and hydraulic motor; and a hydraulic brake on the fluid return line. A method of providing a pump jack assembly includes replacing a non hydraulic pump jack motor, connected to rock the horsehead, with a hydraulic motor.