SummaryModern rocking and stepping cores have been known as the efficient self‐centering earthquake‐resisting systems (SC‐ERSs). The current article proposes an approximate equivalent linear (EL) model for rapid estimation of the SC‐ERS displacement. An equivalent damping ratio and effective stiffness are formulated for flag‐shaped hysteresis of a fully SC‐ERS. The approximate EL model is first established using secant stiffness and Jacobsen's damping model. Nonlinear response history analyses are carried out to compare exact and approximated peak displacements. Findings reveal that EL analysis of the SC‐ERS based on Jacobsen's damping leads to underestimation of the maximum inelastic displacement. Accordingly, a new optimal damping formula is proposed using a genetic algorithm and nonlinear regression analyses. The improved EL model is validated by practical examples, and the results show acceptable accuracy in design‐level displacement estimation.