Despite the extreme precautions that are usually taken in the^design and construction of nuclear power plant containment^vessels, there is still a non-zero probability of radioactivity leakage^from the containment. In view of this, a best estimate and uncertainty^assessment of the containment structural resistance is needed.^Finite element analysis has been considered the most powerful^technique to analyze this type of structure. Such a method is^expensive, particularly when all possible failure modes are required^for the uncertainty analysis; therefore, an alternative approach is^useful. Simplified methods based upon limit analysis theories that^take into account the effects of large deformations are presented.^Methods for the prediction of the strength of stiffened containment^vessels under uniform static internal pressure are developed. Finite^element analyses are used to guide the formulation and calibration^of these methods. Simplified dynamic analyses of locally loaded^cylindrical shells, spherical shells and circular plates are given. The^dynamic solutions are obtained by idealizing the system as a single^degree of freedom model. Several numerical examples are presented^to illustrate the use of the proposed simplified dynamic and staticanalysis methods. Finally, a study of different reliability approachesis conducted. An advanced first order second moment reliabilitymethod and a simplified approach are confirmed by Monte Carlosimulation. These approaches, in conjunction with the simplifiedstructural analysis method, are used to perform the uncertainty;analysis of the resistance of a typical containment vessel;*USDOE Report IS-T-997. This work was performed under Contract W-7405-eng-82 with the U.S. Department of Energy.