The focus of this study is estimating inelastic deformations of building frames by conducting response spectrum analysis. Damping spectra (R-mu-xi-Tspectra) are derived first for SDOF systems defined with their initial period or initial stiffness, in order to attain equal maximum displacements of the companion inelastic systems. Mean spectral relations and their standard deviations are calculated for 566 horizontal pairs of near-fault ground motions. They are further classified with respect to ductility reduction factorR(mu)as well as the earthquake magnitude and soil type, which are found to have notable influence on the effect of damping in reducing maximum displacement. Optimal damping scaling factors are then calculated for converting the standard 5% damped linear elastic spectra to inelastic spectra. Finally, maximum deformations of MDOF building frames are estimated by using the optimal spectral factors through mode superposition analysis. The results are compared with the results obtained from nonlinear response history analysis under different sets of strong ground motions. Mean inelastic deformations are predicted with reasonable accuracy with the proposed procedure. Hence, damping spectra furnishing optimal damping ratios are suggested as a practical tool for assessing the seismic performance of newly designed, code conforming structures.