In this paper, previously developed analytical approach (Chitkara NR, Celik KF. Int J Mech Sci 2000; 42:273) based on the upper-bound theory was applied to analyse the mechanics of the extrusion of non-symmetric U- and I-shaped sections and the symmetric ones from initially round billets through the ruled-surface dies. To investigate the optimum shape of the designed extrusion dies, that yield the lowest upper-bound for a given reduction in area, die length, off-centric positioning and frictional conditions a computer program was developed. Computations were carried out for various cases and some of the results compared with the experimental verifications. Curvature of the extruded product and simulated deforming grid patterns were also predicted and compared. A sophisticated CAD/CAM package was used in conjunction with the CNC and EDM processes to design and manufacture the streamlined dies for the extrusion of some non-symmetric U- and I-shaped sections. The theoretical predictions were observed to be in good agreement with the experimental results. (C) 2002 Elsevier Science Ltd. All rights reserved.