AbstractResults of an analytical study aimed at evaluating residual displacement ratios, Cr, which allow the estimation of residual displacement demands from maximum elastic displacement demands is presented. Residual displacement ratios were computed using response time‐history analyses of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to an ensemble of 240 earthquake ground motions recorded in stations placed on firm sites. The results were statistically organized to evaluate the influence of the following parameters: period of vibration, level of relative lateral strength, site conditions, earthquake magnitude, and distance to the source. In addition, the influence of post‐yield stiffness ratio in bilinear systems and of the unloading stiffness in stiffness‐degrading systems was also investigated. A special emphasis is given to the uncertainty of these ratios. From this study, it is concluded that mean residual displacement ratios are more sensitive to changes in local site conditions, earthquake magnitude, distance to the source range and hysteretic behaviour than mean inelastic displacement ratios. In particular, residual displacement ratios exhibit large levels of record‐to‐record variability and, therefore, this dispersion should be taken into account when estimating residual displacements. A simplified expression is presented to estimate mean residual displacements ratios for elastoplastic systems during the evaluation of existing structures built on firm soil sites. Copyright © 2005 John Wiley & Sons, Ltd.