This lecture reviews new developments in analysis and design of prestressed concrete reactor vessels (PCRV). After a brief assessment of the current status and experience, the advantages, disadvantages, and especially the safety features of PCRV, are discussed. Attention is then focused on the design of penetrations and openings, and on the design for high-temperature resistance -areas in which further developments are needed. Various possible designs for high-temperature exposure of concrete in a hypothetical accident are analyzed. Considered are not only PCRVs for gas-cooled reactors (GCR), but also guard vessels for liquid metal fast breeder reactors (LMFBR), for which designs mitigating the adverse effects of molten sodium, molten steel, and core melt are surveyed. Realistic analysis of these problems requires further development in the knowledge of material behavior and its mathematical modeling. Recent advances in the modeling of high-temperature response of concrete, including pore water transfer, pore pressure, creep and shrinkage are outlined. This is followed by a discussion of new developments in the analysis of cracking of concrete, where the need of switching from stress criteria to energy criteria for fracture is emphasized. The lecture concludes with a brief discussion of long-time behavior, the effect of aging, and probabilistic analysis of creep.