In a machine press with a lower and an upper tool support, a closed hydraulic drive system acts upon the upper tool support. This system has at least one hydraulic drive unit, which includes at least one hydraulic cylinder-piston unit and at least one hydraulic assembly acting upon this unit and supplied from a storage reservoir. A base pressure above environmental pressure constantly prevails in the storage reservoir. The storage reservoir is designed as a cylinder store with a hydraulic chamber defined by a cylinder and a piston unit displaceably guided therein. The piston unit is acted upon on its side functionally opposite the hydraulic chamber by a hydraulic fluid chamber which for its part is connected to a high-pressure gas store. The active surface of the hydraulic fluid chamber on the piston unit is small compared to the active surface of the hydraulic chamber on the piston unit.