In performance-based seismic design, it is clear that the evaluation of the nonlinear response is required. One of the most accurate earthquake analysis method for the performance evaluation of structure is nonlinear response history analysis, but it is time-consuming and necessitate more efforts. Approximate methods are presented for estimating the capacity of structures while subjecting earthquake ground motions. This is made possible by exploiting the connection between the nonlinear static response of structure and the dynamic response of SDF system whose backbone matches the structure’s pushover curve. The nonlinear direct spectrum method(NDSM) and the uncoupled modal response history analysis(UMRHA) are proposed and studied to evaluate nonlinear response of structures, without iterative computations, given by the structural linear vibration period and yield strength from the pushover analysis. In this study, it is to compare the practicality and the reliability of approximate nonlinear methods with respect to mixed building structures and various earthquakes.