Nuclear material containment buildings are required to be periodically inspected to assure good quality conditions. To this end, there is increasing interest in developing efficient and economical testing techniques to monitor and inspect these structures. In this paper we study the dynamic behavior of a 1/3 mock-up containment structure and its internal pressure-dependence using testing techniques that may not interfere with the structure’s operation. The goal is to assess the possibility of monitoring internal pressure and potential leakage by measuring the structural frequency of vibration. The Vercors mock-up structure, a post-tensioned double-wall concrete structure of dimensions 15 m diameter and 30 m tall, was internally pressurized from 0 to 4 bar. We attached a pair of accelerometers at the outer surface of the inner structure and recorded signals periodically without imposing any controlled dynamic input; thus, we used an output-only dynamic analysis. We found that there is a clear positive correlation between internal pressure and the identified frequencies of vibration. We developed a multi-variable correlation, using several frequencies of vibration and the measured pressure, which could be used to monitor internal pressure. To study the underlying physical behavior, we built a finite element model. The observed frequency shift due to applied internal pressure could be partially explained by the effect of geometric nonlinearity, but it does not explain the entire range of frequency shift. Material nonlinearity should also be considered to assess this problem.