<p>The self-centering (SC) hysteretic damper can effectively enhance the seismic resilience of structures, due to its supplemental damping and recentering capability. Recently, a new SC damper, is developed known as the SC Disc Slit Damper (SC-DSD) was experimentally tested using cyclic loading test. In the proposed damper, the steel slit dampers play the role of energy dissipation (ED) source, while the pre-compressed disc spring stacks form the SC system. The tests have shown that the telescopic configuration of the damper ensures a symmetric cyclic behavior. However, additional analytical and finite element (FE) analyses are required to more deeply explore the effects of the damper's parameters and its local behavior. Based on the working mechanism of the damper, the restoring force models of the ED system and SC system are first derived individually, and then they are combined to obtain the hysteretic model of the damper. In addition, the FE model of the damper is established to provide additional information that is challengeable to observe in tests. The accuracy of the analytical method and FE model is confirmed by the testing results. Further, the parametric analysis is conducted based on the validated FE model, using the key parameters of the length of the steel strips, the width of the steel strips, and the preload of the stacked disc springs. Based on this work, the hysteretic behavior of the damper is further understood, and more importantly, it provides more insights for practical applications of the damper.</p>