In order to evaluate the limit earthquake resistance of multi-story steel frames influenced by the strength and stiffness ratios of members, a series inelastic response analysis were carried out. From the analysis results, the damage distribution rules of multi-story steel frames were proposed. Conclusions are summarized as follows; 1)As the stiffness ratios of beam and column becomes small, the damage concentrates on the lower end of columns of the first story. 2) Considering the strength and stiffness ratios of the beam and column with weak beam type mechanism, the equations predicting the damage distribution of multi-story steel flames were proposed. 3) Through the equation which was supposed in this study, it is speculated that the damage distribution of the rigid or semirigid beam collapse type multi-story steel structure building can be predicted.