Abstract: The piston of a pile driving hammer is raised by hydraulic (water) pressure. As the hammer is permitted to fall, the water pressure is diverted from the cylinder, until the cycle begins again. Pressure surges, upon switching to and from pressure diversion, are turned to advantage by providing large pressure vessels with bag accumulators upstream and downstream of the hydraulic pressure supply pump. The water pressure is selectively throttled to control the frequency and amplitude of the stroke. The pressure vessel may be a pressure tank containing an air cushion. In this way, much of the pressure accumulated or reduced while the pump is working against an isolated pressure vessel acts in concert with the pump to advance the water when the respective pressure vessel is reconnected.