A mathematical model is given for the metal forming in an axisymmetric nonconical converging die. By using the Maple V system a semianalytical algorithm is proposed for the calculation of the optimal shape of the die which minimizes the consumed energy of the deformation and the power of the friction forces at the wall. Two examples are presented to demonstrate the efficiency of the proposed method. © 1999 Elsevier Science Ltd and Civil-Comp Ltd. All rights reserved.