In this study, residual displacement demands are investigated for SDOF systems with period range of 0.1-3.0 s for near-field and far-field ground motions. The effects of stiffness degradation and post yield stiffness ratio on residual displacements are investigated. The modified-Clough model is used to represent structures that exhibit significant stiffness degradation when subjected to reverse cyclic loading. An elastoplastic model is used to represent non-degrading structures. For inelastic time history analyses, Newmark’s step by step time integration method was adapted in an in-house computer program. Based on time history analyses, a new simple equation is proposed for residual displacement demand of a system as a function of structural period (T), ductility (µ), strain hardening ratio (α) and spectral displacement (S d ).