Abstract: If the displacement of rubber bearing of base- isolated buildings, which is usually caused by some what resonance effect from long period ground motion, the additional stiffness components will work together with rubber bearings and then the possibility of further increase of the displacement of rubber bearing is suppressed and reaches the prescribed limitation because the natural period of the base isolation building has been changed. However the extra stiffness would let the story shear forces of the super-structure slightly increase. A mult-i particle structural analytic model is set up. The motion equations of three states of non- affixation, right affixation and left affixation are deduced, and the computer program is developed. On the basis of exemplary analysis for typical base- isolated building , the effectiveness of the device in limitation of developing large lateral displacement of rubber bearing is demonstrated and the way of choosing appropriate parameters for the protective device is discussed.