In the seismic upgrading design of existing steel arch bridges if it is difficult to prevent damages to the secondary members such as braces, bridges are designed allowing damages to the secondary members while ensuring the safety of the structure. In such a case, it is important to accurately predict the behavior in the post-peak regions of the secondary members in the seismic response analysis. In this study, the applicability of an analytical model that can accurately and easily predict the post-peak behavior of the secondary members is discussed. As a result, the post-peak behavior of the secondary members could be accurately predicted by the numerical model investigated, if the effective slenderness ratio of the secondary members is appropriately evaluated.