Abstract: The shape sensitivity analysis of high-temperature extrusion processes and its applications to the optimum design of the tool shape are discussed. A numerical method is proposed for the shape sensitivity analysis of the stationary inelastic deformation processes of the strain rate dependent materials, and the efficiency of this approach is compared with that of the finite difference method. The mathematical model and the numerical solution techniques of the tool shape design optimization are presented. A numerical example with regard to a 2-dimensional extrusion die design problem illustrates the validity of the problem formulation and the efficiency of the present method.