In the present investigation, an analysis using three-dimensional upper-bound method based on continuous velocity filed has been carried out for the extrusion of circular, square, and rhomboidal sections from round billets. The die surface representation in the present work could easily be applied to the extrusion of many different shapes just by defining the functions that describe the entry and exit sections and putting them into the general formulation. The die profile was tested for the third- and fifth-order polynomial functions. The extrusion process is also simulated using the finite element code, ansys (V 14.0), in order to assist the mathematical solution and to show the stress and strain distributions for the products when the strain hardening effect is taking into the account. Effects of friction, shape complexity, reduction of area, and die length on the extrusion pressure were also investigated. The results obtained in this work were compared with the theoretical results of other workers and found to be in highly compatible.

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