A finite element analytical model involving an explicit time integration procedure is used to treat a prestressed concrete reactor vessel (PCRV) for liquid-metal fast breeder reactor containment. The model is axisymmetric and includes simulations of the tensile cracking of concrete, the reinforcement, and a prestressing capability under transient load. The quasi-static prestressing operation of the PCRV model is performed by an improved dynamic relaxation technique. The concrete material model used in these analyses accounts for tensile cracking in arbitrary directions, crushing of concrete, and the reinforcing steel The variation of the concrete tensile cracking limit with strain rate is taken into account. The prestressing tendons are modeled and relative slip is permitted. Several example solutions using the analytical model were compared with experimental results. The comparisons included simply supported beams and also small scale models of PCR Vs. It was shown that the analytical methods correlate quite well with experimental results, although in the vicinity of the failure load, the response of the models tends to be quite sensitive to input parameters.