A press machine is provided. Two vertical hydraulic cylinders are arranged on an upper beam plate of a press machine body, and the two hydraulic cylinders correspond to workbenches at corresponding positions in a one-to-one correspondence, constituting left and right working units, and a common mechanical drive unit and a common hydraulic drive unit are set for the left and right working units. The mechanical driving unit is composed of a driving motor through an electromagnetic clutch, an electromagnetic brake and lead screw nut driving mechanism driven by a gear pair. According to the load profiles during the working process of hydraulic press machine, the mechanical driving unit or the hydraulic driving unit are selected to provide energy for the two working units. A control method for the press machine, a press machine execution system and a control method for the press machine execution system are further involved.