Abstract This study proposes a procedure for determining design input energy spectra for self-centering single-degree-of-freedom (SDOF) systems using a characteristic flag-shaped hysteretic model. The procedure for determining design input energy spectra considers the influence of ground motion factors, hysteretic models, damping ratios, and ductility factors. First, nonlinear dynamic time history analyses are performed using 40 representative ground motion records to establish the relationship between input energy spectra and critical parameters. Based on this, normalized design input energy spectra and relevant parameters are proposed. The results of this study indicate that the bilinear hysteretic model is not suitable to accurately predict the input energy spectra for self-centering systems. Meanwhile, both the damping ratio and ductility factor have a significant influence on the resulting input energy spectra throughout the entire period range. The proposed procedure can be used to predict earthquake input energy spectra for self-centering SDOF systems.