Equal channel angular extrusion (ECAE) or pressing is a process used to introduce severe plastic deformations to processed materials with the aim of improving their mechanical properties by reducing the grain size. At present, there are no analytical studies that have considered strain hardening materials in order to determine the required force to carry out the process. All the existing papers have only considered nonstrain hardening materials. Furthermore, all those studies have been done by considering plane strain conditions. In this work, an upper bound analysis of the required force for performing the ECAE process is made by considering a full three-dimensional geometry with a rectangular cross section. From this analysis, the influence of the geometric and the material parameters is studied by considering both friction and strain hardening materials. By using the upper bound method, an analytical formulation was obtained and the influence of all the parameters was determined. With this work, it is possible to have a wider knowledge of the influence of the main affecting parameters in the ECAE process and to optimize them.