A high-pressure system for hydroshaping a hollow workpiece has a lower die and an upper die vertically shiftable above the lower die and forming therewith a cavity shaped to hold the workpiece. An upper actuating element bears downward via a vertically compressible hydraulic operating cylinder on the upper die. A spring-loaded pressure-storing cylinder is connected by a hydraulic line to the operating cylinder and to the workpiece. Downward shifting of the actuating element first closes the dies together, then internally pressurizes the workpiece via the line from the operating cylinder such that the workpiece deforms and shapes itself to the cavity, and then fills the spring-loaded pressure-storing cylinder. Subsequent upward shifting of the actuating element at first allows the pressure-storing cylinder to empty, and then entrains the upper die upward off the workpiece by the actuating element.