In this work, a method for calculation of the optimal shapes of axisymmetrical converging dies by an adaptive finite element method is presented. The shape optimization problem considered in this paper is to find the best shape of the die such that the flow rate will be uniform at the die exit.The optimization problem is to minimize an objective function by varying a part of boundary (ie: the shape of die) subject to constraints imposed by the metal forming problem. In this method, the B-spline functions allow us to determine the shape of the die, using its control points as design variables. An adaptive solution procedure is adapted to control the error due to the finite element approximation. The mesh adaptation is performed using the Zienkiewicz - Zhu (Z²) type error estimator. © 2009 American Institute of Physics.