The seismic safety of reinforced concrete containment building can be evaluated by probabilistic analysis considering randomness of earthquake, which is more rational than deterministic analysis. In the safety assessment of earthquake-resistant structures by the deterministic theory, it is not easy to consider the effects of random variables but the reliability theory and random vibration theory are useful to assess the seismic safety with considering random effects. The reliability assessment of reinforced concrete containment building subjected to earthquake load includes the structural analysis considering random variables such as load, resistance and analysis method, the definition of limit states and the reliability analysis. The reliability analysis procedure requires much time and labor and also needs to get the high confidence in results. In this study, random vibration analysis of containment building is performed with random variables as earthquake load, concrete compressive strength, modal damping ratio. The seismic responses of critical elements of structure are approximated at the most probable failure point by the response surface method. The response surface method helps to figure out the quantitative characteristics of structural response variability. And the limit state is defined as the failure surface of concrete under multi-axial stress, finally the limit state probability of failure can be obtained simply by first-order second moment method. The reliability analysis for the multiaxial strength limit state and the uniaxial strength limit state is performed and the results are compared with each other. This study concludes that the multiaxial failure criterion is a likely limit state to predict concrete failure strength under combined state of stresses and the reliability analysis results are compatible with the fact that the maximum compressive strength of concrete under biaxial compression state increases.