Optimal shapes are found for the flange of an H-beam. A forced displacement is given at the free end of the cantilever beam so that the average deformation angle reaches the specified value. The objective function to be maximized is the dissipated energy, and a constraint is given for the maximum equivalent plastic strain at the fixed end. Globally optimal solutions are searched by a simulated annealing, which is successfully combined with a commercial finite element analysis code. It is shown that the energy dissipation capacity is significantly improved by optimizing the flange shape.