Abstract: The residual displacement ratio is defined for the bilinear single degree of freedom (SDOF) system, and the equal strength residual displacement ratio spectrum is constructed by means of elasto-plastic time history analyses using 100 earthquake records. The factors influencing the spectrum are analyzed and the corresponding fitting formulas are established. Finally, the relationship between the residual displacement and the maximum displacement is studied. The results indicate that, on the whole, the smaller the period, strength, or the post-yielding stiffness coefficient, the larger the residual displacement factor. When the structural period is relatively large, the residual displacement factor is basically independent of the period. The smaller the period is, the greater the structural strength influences the residual displacement factor. In addition, the residual displacement basically has a linear relationship with the maximum displacement.