to the atmospheric level in order to unlock the bar 14 and enable the bar flange 20 and the vessels 3 to be forced by the springs 16 upward until the seal 5 on the flange 20 and the edges of the vessels 3 come into close contact with the blank 4 dividing same into a plurality of zones after that the liquid from the pressurized supply 6 is supplied successively into each of the cavities a the pressure value being regulated by the reducing valves 8 the pressure in each cavity a depends on the shape of the part being extruded on the mechanical properties of the blank material its thickness and the radius of curvature of the part in each zone this pressure value is determined by computation as the pressure in the cavities a varies the blank 4 is being shaped into the required part the evolving shape periodically checked by applying the template 21 as the liquid is simultaneously supplied under different pressures to different zones of the blank 4 the thickness of the billet is changed uniformly in the process of deformation as a result the part produced has a wall thickness within reasonable limits of accuracy to prevent loss of stability of that zone of the blank 4 which adjoins the clamping means 12 as the part is being extruded this zone is deformed at a pressure somewhat higher than that required for its deformation the central zones of the blank 4 experience a pressure not exceeding the deformation pressure upon completion of the hydraulic extrusion process the reducing valves 3 are closed and the valves of the conduits 7 are opened causing part of the liquid to flow out of all cavities a and out of.