Abstract: A hydraulic pump jack drive system for reciprocating an oil well pump rod. The drive system comprises at least one hydraulic well head cylinder, a reversible flow hydraulic pump, and a master cylinder. The master cylinder has a free floating master piston and at least one fixed bulkhead. The master cylinder also has a working fluid chamber hydraulically connected to the hydraulic well head cylinder and at least two master piston drive chambers hydraulically connected to the hydraulic pump. The hydraulic well head cylinder and the working fluid chamber are filled with a working fluid and define a working fluid system while the master piston drive chambers and the hydraulic pump are filled with hydraulic fluid and define a hydraulic drive system. Reversing the flow of the hydraulic pump causes the master piston drive chambers to be pressurized and de-pressurized on an alternating basis to reciprocally move the master piston within the master cylinder.