Abstract A transfer function of absolute acceleration response of NSC which is supported on a base-isolated structure is presented. Base flexibility has been assumed to be described by complex-valued impedance function which calculated by cone model. The proposed formulation is used to generate the FRS by PSDF according to random vibration theory, and compared with the FRS obtained by the time history analysis. The results show that PSDF provides satisfying FRS with far less effort and good agreement with current seismic code; The peak acceleration of NSC is appear in low frequency band(near base-isolated frequency), and the use of base-isolated device would weakening the effect of SSI, especially in the base-isolated frequency band.