[en] This paper outlines an analytical and numerical procedure developed for the frequency domain finite element analysis of category I nuclear structures, in particular, of reinforced concrete containment shell structures, subjected to earthquake ground acceleration. Such a procedure can be conveniently used in the analytical evaluation of the overall seismic safety of nuclear power plant structures. Emphasized in this presentation, however, is the analytical procedure associated with the random vibration analysis. The earthquake ground acceleration is assumed to be a Gaussian vector process characterized by a zero mean and three-by-three cross-spectral density matrix of its three components. A SAP V finite shell element code is used to evaluate the natural frequencies and modes that are significantly participating