A method for modifying a work piece, the method comprising: a) providing a die including a first die plate and a second die plate, wherein at least one of the first and second die plates is movable relative to the other between an open position and a closed position wherein the first and second die plates together define a die cavity; b) positioning the work piece in the die cavity; c) generating a traveling shock wave by generating an explosion of gaseous combustibles, wherein the shock wave has a length that is smaller than the length of a shock wave travel path relative to the work piece; d) conveying the shock wave along the work piece to progressively apply a localized pressure against the work piece; e) holding the first and second die plates (164, 166) in the closed position with a selected die holding force against pressure from the shock wave in a direction that is transverse to the shock wave path of travel throughout step d), wherein the die holding force is correlated to a filling pressure of the gaseous combustibles and the pressure and length of the shock wave; and f) ejecting the work piece from the die cavity after step d), wherein the method further comprises: g) providing an ignition chamber in which the shock wave is generated; h) isolating the ignition chamber from the die prior to step c); i) transferring combustibles into the ignition chamber after step h); j) fluidly connecting the ignition chamber with the work piece after steps b) and i), k) filling the work piece with incompressible fluid prior to step c); I) transferring the shock wave from a gas into the incompressible fluid prior to step d), and wherein step c) includes generating an explosion with the combustibles to generate the shock wave after step j). a) providing a die including a first die plate and a second die plate, wherein at least one of the first and second die plates is movable relative to the other between an open position and a closed position wherein the first and second die plates together define a die cavity; b) positioning the work piece in the die cavity; c) generating a traveling shock wave by generating an explosion of gaseous combustibles, wherein the shock wave has a length that is smaller than the length of a shock wave travel path relative to the work piece; d) conveying the shock wave along the work piece to progressively apply a localized pressure against the work piece; e) holding the first and second die plates (164, 166) in the closed position with a selected die holding force against pressure from the shock wave in a direction that is transverse to the shock wave path of travel throughout step d), wherein the die holding force is correlated to a filling pressure of the gaseous combustibles and the pressure and length of the shock wave; and f) ejecting the work piece from the die cavity after step d), g) providing an ignition chamber in which the shock wave is generated; h) isolating the ignition chamber from the die prior to step c); i) transferring combustibles into the ignition chamber after step h); j) fluidly connecting the ignition chamber with the work piece after steps b) and i), k) filling the work piece with incompressible fluid prior to step c); I) transferring the shock wave from a gas into the incompressible fluid prior to step d),