In the design of seismic isolation systems, one of the key and most difficult issues is the damping optimal parameters choice. If the damping is negligible, it is possible (at a certain frequency of external influence) that quasi-resonant processes, which lead to the disappearance of seismic insulation effect, will emerge. If the damping forces are large, it entails a significant load increase on the protected object, which also reduces the effect of seismic insulation. Development technique of plastic dampers analytic dependence «force-displacement» executed as linear or nonlinear quarter circle cores is presented in the research. These dependences are applied to choose rational parameters of pendular type of seismic insulation system damping.