An apparatus and method for swaging a square or rectangular tube, the apparatus including a support for external dies, both surface dies and corner dies, which when actuated, apply pressure to the outside of a tube to achieve its swaging to a lesser dimension, and having a collapsible mandrel located therein, supporting internal dies, that apply a lesser pressure against the interior of the tube, during a swaging operation, to assure that wall buckling does not occur. An internal die with its removing tool may locate within the end of the tube to be swaged to cooperate with the pressure from the external dies to swage the tube without any final buckling.