The floor response spectra are calculated by constructing a numerical model (APR1400) equipped with base isolators of a bilinear material and a Bouc-Wen material, respectively, in order to investigate the effect of the second hardening. The variations of the earthquakes are incorporated to the loads, and two different properties of the isolator materials are modeled. The second hardening behavior increases the stiffness of the isolator in the high strain regime and suppresses the displacement of the isolator. Therefore, the role of the base isolation device isolating the superstructure from the ground motion does not perform properly, which causes amplification of the floor response of the superstructure. In practice, the second hardening of the isolator material might need to be taken into account for designing the base isolation system.