The possibility of conservation of the potential energy part of elastic strains accumulated at the end of the working stroke of the press in its metal structures and in the working fluid by means connecting the cavities of the working hydraulic cylinders with the fluid cavity of hydraulic device with elastic properties (energy storage) is considered. Dimensionless calculated dependencies are obtained and analyzed to determine: increments of the potential energy of elastic strains of the storage device; the residual potential energy of elastic strains of the metal structures of the press and working hydraulic cylinders with the working fluid contained in them; energy losses — at the end of the pressures equalization in the cavities of the working hydraulic cylinders of the press and storage.