For the overall safety evaluation of seismic category I structures subjected to various load combinations, a quantitative measure of the structural reliability in terms of a limit state probability can be conveniently used. For this purpose, the reliability analysis method for dynamic loads, which has recently been developed by the authors, was combined with the existing standard reliability analysis procedure for static and quasi-static loads. The significant parameters that enter into the analysis are: the rate at which each load (dead load, accidental internal pressure, earthquake, etc.) will occur, its duration and intensity. All these parameters are basically random variables for most of the loads to be considered. For dynamic loads, the overall intensity is usually characterized not only by their dynamic components but also by their static components. The structure considered in the present paper is a reinforced concrete containment structure subjected to various static and dynamic loads such as dead loads, accidental pressure, earthquake acceleration, etc. Computations are performed to evaluate the limit state probabilities under each load combination separately and also under all possible combinations of such loads.