In this research, the threshold stiffness and residual displacement of the MPCFS are both investigated. The MPCFS has a higher threshold (breakaway) stiffness and no residual displacement after earthquakes or ambient vibrations, which makes it different from the conventional Curved Surface Slider (CSS). These two features can enable the MPCFS to be more stable when experiencing micro-to-small shakings, and always restore to its central point after earthquakes. With the aim of testifying the two features, a series of analytical simulations are conducted on a four-storey building model equipped with MPCFS. The analytical results are compared with that obtained with CSS. The simulation results validate the aforementioned virtues of MPCFS over the CSS. This indicates that MPCFS has great potential in the engineering practice of seismic isolation.