Seismic structural fuses such as buckling restrained braces (BRBs) are highly nonlinear members that need a detailed finite element model (FEM) to represent their actual behavior. On the other hand, making detailed model for the whole building from solid or shell elements to be consistent with the model of BRBs would require expensive computational time and large storage space especially when performing nonlinear time history analysis (NTHA). Therefore, a mixed FEM is developed in this research so that the solid elements are used for the core plate and the restraining system only. The non-yielding segments of the BRBs and the conjoined girders and columns are simulated using beam elements with nonlinear material properties while the effect of large deformations is taken during analysis and this was able to represent plastic hinge formation, plastic rotations and residual displacements in such members. A beam-solid transfer mechanism is developed to properly transfer forces between the non-yielding segments of BRB and the inner solid plate. The core plate is connected to the surrounding restraining system with contact elements to simulate the normal and frictional forces generated upon contact based on the penalty algorithm. This model was validated using the data and the results of an experimental work mentioned in the literature where very good agreement was achieved. Thereafter, a rehabilitation study for the SAC 9-storey building was performed. The results showed how the BRBs work as structural fuses during earthquakes and confirmed the ability of the model to represent inelastic behavior of multi-story BRBFs.