Abstract: Based on elastic-plastic time-history earthquake analysis of the single degree of freedom (SDOF) system, the seismic-force-modification factor R of the bilinear elastic-plastic model was investigated for different site types, natural vibration periods, ductility, damping ratios and post-yield stiffness ratios. It is found that the most important factor determining R is the ductility, and that damping and the post yield stiffness have only a minor effect in the short period range. In the long period range, the damping has negligible effect on R spectra. The characteristic period Tg of the site was analyzed using six different approaches, among which five methods get the identical Tg. This Tg was used to normalize R spectra to maintain the peak phenomena near Tg. The probability distribution of R factor appears to be consistent with the lognormal distribution. Simplified formulae are proposed for Rμ spectra.