Current design procedures for nuclear containment vessels are based on elastic analyses. Though such techniques are adequate under normal operating conditions, if the potential risks associated with extreme environments or accident conditions are to be assessed, knowledge of the ultimate capacity of the containment structure is essential. A key technical question is whether penetrations, such as personnel hatches, weaken the containment structure. In this paper, the maximum pressure sustained by a scale model, steel, nuclear containment vessel with a penetration is determined using a three-dimensional finite element analysis. To assess containment strength, a clean shell is analyzed in closed form for its ultimate strength, and the solution is then compared with finite element results for a structure that has a penetration. The comparison shows that the personnel hatch penetration does not reduce the ultimate strength of the containment structure. In this paper, it is assumed that the materials have no flaws and welded joints are perfectly bonded. Cracks in the structure, which would degrade its strength, are not considered.