A deep well hydraulic pump system using a high pressure accumulator, comprises a down hole pump which is lowered on tubing into the borehole and has a large cylinder and piston connected to a small cylinder and piston with a common piston rod. The large cylinder is connected to the surface by a liquid pipe inside of the tubing. A surface motor-driven pump in one part of the pumping cycle takes liquid from which a high pressure accumulates and pumps it at high pressure through the liquid pipe into the large cylinder, forcing the piston down, and forcing well liquid up the tubing. Part of this liquid goes to a sump and part goes through a pressure sensitive valve to storage. In the second part of the cycle the surface pump draws from the sump and pumps liquid down the tubing. This raises the piston in the large cylinder and lifts liquid through the foot valve into the small cylinder, ready for the next repetition of the two-part cycle. The liquid pumped from the large cylinder flows into the high pressure accumulator.