A method of pumping oil from wells by using a downhole pump without sucker rods. Subsurface hydraulic pumps consist of two reciprocating pumps coupled and placed in the well. One pump functions as an engine and drives the other pump (the production pump). The downhole engine is usually operated by clean crude oil under under pressure (power oil) that is drawn from a power-oil settling tank by a triplex plunger pump on the surface. If a single string of tubing is used, power oil is pumped down the tubing string to the pump, which is seated in the string, and a mixture of power oil and produced fluid is returned through the casing-tubing annulus. If two parallel strings are used, one supplies power oil to the pump while the other returns the exhaust and produced oil to the surface. A hydraulic pump may be used to pump several wells from a central source.