In this research topology optimization approach has been used to determine suitable configurations for a multy-storysteel structures under seismic excitation. Since the nonlinear behavior of the material playes an important role in the response of the structure, an indirect scheme, assuming elastic behavior, has been employed to minimize the maximum displacements of the stories. Instead of minimizing the displacements, which are obviously history dependent, the objective of optimization process has been considered ,implicitly, to be the maximization of energy dissipation when the structure begins to experience the first cycle of the yielding. An elastic analysis has been used during the optimization process to proceed towards the objective of the problem (i.e. maximization of the volume of the yielding materials. Spectral analyses have been performed to calculate the earthquake loads using some available well-known response spectrums. For further use in sensitivity analysis, the spectrums have been smoothed via fitting polynomials. Finite element method has been employed for stress analysis during the optimization process. The thickness of the element has been considered as the design variable and the sensitivity of the objective functio has been evalulated by a general sensitivity analysis for the earthquake load through calculation of the sensitivities of the natural frequencies. The results have been obtained and discussed for several multy-story structures. To show the performance of the indirect optimization procedure, the reduction in the response of the structures have been examined through time-domain analyses. It is shown that the proposed process is successful in decreasing the maximum displacements when comparing the response of the optimal configuration with those of some conventional structural systems. To recommend a suitable factor for the loads in design of the structures for maximum dissipation of the energy, the optimization problem has been solved for several fractions of the loads followed by the time domain response analysis. The results illustrate that for the most of the studied cases the designs based on an optimal fraction of the earthquake loads show maximum reduction in the response of the structures.