•A new modified flag-shape (MFS) model and its equivalent linearization interpretation is proposed.•The effectiveness of the MFS model and the corresponding equivalent linearization coefficients is verified.•Optimization using the MFS model subject to stochastic excitation demonstrate more economic ductility demand in structural design. The analysis and design of self-centering structural systems have attracted substantial attention from researchers for the seismic design of structures. The flag-shaped hysteretic model has been widely used in the design and structural response analysis of self-centering devices. In this research, a modified flag-shaped (MFS) model is proposed to describe the hysteretic characteristics of self-centering energy dissipation (SCED) braces, which are commonly used in self-centering structures. The MFS model comprises three parts: a linear elastic part, a bilinear elastic part, and an elasto-plastic part with a slip zone. The effectiveness of the MFS model is validated based on the results of the quasi-static and hybrid simulation tests available in the literature. Equivalent linearization is carried out on the MFS model for stochastic earthquakes, and closed-form solutions are obtained for the linearized parameters. A one-degree-of-freedom braced system is used to verify the equivalent linearization of the MFS model in comparison with Monte Carlo simulation results. Finally, an SCED-braced five-story frame structure is optimized by minimizing the maximum ductility demand for the SCED braces using the equivalent linearization of the MFS model. The optimized design by the MFS model is observed to exhibit uniform ductility demands along the height. This can be considered as the ideal optimal solution. The responses of the multi-degree-of-freedom structure also demonstrate the effectiveness of the proposed MFS model and its equivalent linearization.