A method and system for pumping unit with an elastic rod system is applied to maximize fluid production. The maximum stroke of the pump and the shortest cycle time are calculated based on all static and dynamic properties of downhole and surface components without a limitation to angular speed of the prime mover. Limitations of structural and fatigue strength are incorporated into the optimization calculation to ensure safe operation while maximizing pumped volume and minimizing energy consumption. Calculated optimal prime mover speed is applied to the sucker rod pump by means of beam pumping, long stroke or hydraulic pumping unit by controlling velocity, acceleration and torque of the electric prime mover or by controlling pressure and flow rate in hydraulically actuated sucker rod pumping system.