The present paper develops a reliability analysis method for category I nuclear structures, particularly for reinforced concrete containment structures subjected to various load combinations. The loads considered here include dead loads, accidental internal pressure and earthquake ground acceleration. For mathematical tractability, an earthquake occurrence is assumed to be governed by the Poisson arrival law, while its acceleration history is idealized as a Gaussian vector process of finite duration. A vector process consists of three component processes, each with zero mean. The second order statistics of this process are specified by a three-by-three spectral density matrix with a multiplying factor representing the overall intensity of the ground acceleration. With respect to accidental internal pressure, the following assumptions are made: (a) it occurs in accordance with the Poisson law; (b) its intensity and duration are random; and (c) its temporal rise and fall behaviors are such that a quasi-static structural analysis applies. A dead load is considered to be a deterministic constant.