Abstract An upper bound-lower bound model based on the “energy method” has been developed for the hemispherical-punch hydroforming processes. This activity is primarily undertaken to help to define either a suitable level of friction or an operating fluid-pressure path for the purposes of process design and control. The punch deforms the workpiece by moving it against a controlled pressurized fluid. As the punch travels, the workpiece is deformed over its central regions into a hemispherical shape initially, the final shape being that of a hemispherical cup. The present parametric study includes a general friction-force expression as well as an explanation of the change of geometries. Loci representing the critical fluid pressures that result in rupture and wrinkling are presented.