When supervising a nuclear power plant, the containment building is crucial. Its functions are guaranteeing structural integrity and avoiding leaks in case of accident. Both events are considered of high risk. Once a given overpressure is registered inside the containment building, three possible outputs are considered: serviceability, breakdown, and collapse. The aim is the study of vulnerability. The vulnerability of the containment building under an overpressure is described by the conditional probability of the three mentioned outputs. The obtained vulnerability model for collapse is similar to previous results in nuclear power plant safety analysis.