There has been an increasing demand for introducing a base isolation system to secure the seismic safety of a nuclear power plant. However, the design criteria and the safety assessment methodology of a base isolated nuclear facility are still being developed. A performance based design concept for the base isolation system needs to be added to the general seismic design procedures. For the base isolation system, the displacement responses of isolators excited by the extended design basis earthquake are important as well as the design displacement. The possible displacement response by the extended design basis earthquake should be limited less than the failure displacement of the isolator. The failure of isolators were investigated by an experimental test to define the ultimate strain level of rubber bearings. The uncertainty analysis, considering the variations of the mechanical properties of isolators and input ground motions, was performed to estimate the probabilistic distribution of the isolator displacement. The relationship of the displacement response by each ground motion level was compared in view of a period elongation and a reduction of damping. Finally, several examples of isolator parameters are calculated and the considerations for an acceptable isolation design is discussed.