SummaryStructures undergoing inelastic displacements during earthquake ground motions are known to sustain some amount of residual displacements, which may make those unusable or unsafe. In this study an attempt is made to estimate residual displacements for elastic‐perfectly‐plastic single‐degree‐of‐freedom oscillators with a given ductility ratio. Such oscillators belong to the class of bilinear hysteresis models applicable to steel structures, with post‐yield‐stiffness ratio taken as zero, and may be used for the conservative estimates of residual displacements when the post‐yield‐stiffness ratio is unlikely to become negative. Statistical estimation of residual displacement spectrum via normalization with respect to inelastic or elastic spectral displacements is considered and expressions are proposed for both types of normalizations. The statistical dependence of residual displacement on the seismological and site parameters and strong motion duration is also studied and a simple scaling model is proposed in terms of earthquake magnitude, epicentral distance, and geologic site condition parameter for the seismic region of western U.S.A. According to this model, the variation of residual displacement with period primarily depends on the site conditions, and the residual displacements are more sensitive to ductility ratio at low ductility ratios.