A die system for full enclosed die forging with an enclosed cavity (1a, 2a) is formed between an upper die (1) attached to the side of a slide (6) and a lower die (2) mounted to the side of a bolster (17). A workpiece stock (7) disposed in the cavity is pressurized to be diverted with an upper counter-punch (8) in the upper die and a lower counter-punch (22) in the lower die and is thereby forged within the confines of the cavity. A pressure means (11, 19) is disposed above the upper die (1) and/or below the lower die (2) for applying pressure to at least one of the upper and lower dies (1, 2) from at least one of their upper and lower sides to act to enclose or close the cavity (1a, 2a) unilaterally or bilaterally. A back pressure imparting means (12, 20) is disposed above the upper counter-punch (8) and/or below the lower counter-punch (22) for applying back pressure to at least one of the upper and lower counter-punches (8, 22) to force the workpiece stock (7) being formed to be diverted unilaterally or bilaterally in the cavity. A back pressure removal means (33, 36) is associated with the back pressure imparting means (12, 20) to remove the back pressure upon the workpiece stock filling the cavity. An ensuing intense force of enclosure provides a forged product that is free of void and is of high quality.