In this research, a topology optimizatio approach has been used to determine the suitable configurations for bracing of multi-story structures under earthquake- induced loads. Minimization of the compliance has been considered as the objective of the optimization process. The material in assumed to exibit an elastic behavior. Spectral analysis have been performed to calculate the earthquake loads using some spectrums have been smoothed via polynomial fitting. Finite element method has been employed for stress analysis during the optimization processes. The thickness of the elements has been considered as the design variable and the sensitivity of the objective function has been evaluated by a general sensitivity analysis for the earthquake load through calculation of the sensitivities of the natural frequencies. As the side constraints, the thickness of the elements and the total volume of the material have been limited to some maximum prescribed values. The results have been obtained and discussed for several multi-story structures.