In this study, based on the random-vibration-theory (RVT) methodology, an earthquake response analysis of a nuclear facility with a rigid foundation on rock/soil sites is considered when incoherent seismic waves are incident on the system. Using the coherency function of seismic waves, the power spectral density (PSD) matrix for six-degree-of-freedom motions of the rigid foundation is calculated. The stochastic earthquake responses of the soil–structure interaction system are obtained, and the PSD function for the pseudo-acceleration of equipment on one floor of the structure is derived. Peak factors of random vibrations are employed to estimate the spectral acceleration or in-structure response spectrum (ISRS) of the equipment. The accuracy of the proposed RVT methodology is verified for nuclear power plant structures on hard rock, soft rock, and layered soil acted upon by coherent and incoherent seismic waves. Because the ISRS outcomes are found to decline at high frequencies, reduction factors due to incoherency are obtained from the proposed RVT methodology. These factors can be applied to earthquake responses to coherent ground motions to consider the effects of incoherent seismic waves.