Determination of total extrusion power and die pressure distribution is very important for die design. In this work, an upper-bound model with strain hardening is proposed, the prediction of the extrusion power of which is as accurate as that determined by the finite-element method (FEM) and is in excellent agreement with published experimental results. The upper-bound model, when combined with the slab method, also predicts the die pressure distribution, which again is in reasonable agreement with FEM results. Further, the computational time taken by the combined upper-bound/slab method is significantly less than that for FEM. The proposed combined upper-bound/slab method is applied to compare eight different die shapes, namely, stream-lined (third and fourth-order polynomial, cosine and modified Blazynski's CRHS), elliptical, hyperbolic, conical and Blazynski's CRHS. Based on the consideration of total extrusion power (under optimal conditions), it is concluded that third- and fourth-order polynomial dies and the cosine die are the best amongst the profiles considered. Parametric study is carried out for the third-order polynomial die to study the effects of reduction ratio, friction factor and strain-hardening on the optimal die length and die pressure distribution. © 1995.