The rupture of an expansion tube is mainly affected by the expansion ratio and the external shape of the punch used to expand the tube. In order to prevent the tube from rupture, the effect of the external shape of the punch should be considered in the design. The aim of this paper is to confirm the effect of key design parameters of the punch on rupture of the tube using a finite element analysis with a ductile damage model. The results of the analysis indicated that the expansion ratio of the tube was mainly affected by variation of the radius of the punch. However, the rupture was more affected by variation of the punch angle than the radius of the punch. The existence of a specific punch angle at which rupture did not occur, even if the radius of the punch was increased, was found from the results.