The high damping rubber bearings contributed to reduce a seismic force transmitted to upper structures, the material properties of rubber changes with time and the rubber with age-related degradation can affect the seismic response of structures and equipments. Therefore the seismic response of structure considering age-related degradation of isolators should be evaluated. In this paper, the stiffness and damping for isolators were defined using the aging data proposed by other researchers. The reactor containment building and the auxiliary building were selected to conduct the nonlinear analysis and the natural frequency, maximum responses, floor response spectrum(FRS) were evaluated with time using the four earthquakes with different frequency contents. According to the analysis results, the seismic responses are increased by the age-related degradation of isolators and the detail inspections should be conducted up to 20 years because it was presented that the change of FRS was high during this period.