[en] Due to their very high energy absorption capability, as well as their inherent safety advantages, prestressed concrete reactor vessels are presently being keenly studied as the basic barrier to contain hypothetical core disruptive accidents in a fast breeder reactor. One problem investigated is the nonlinear constitutive behavior and failure criteria for concrete. Previously, a comprehensive theory, called endochronic theory, has been shown to satisfy all basic currently known features of test data. Nevertheless uncertainty still exists with regard to non-proportional loading paths, for which good test data are lacking at present. An extension of the endochronic theory which correlates best with general experimental evidence and includes fracturing terms is given, and a comparison with vertex-type hardening in plasticity is made. A second problem which must be analysed in accident situations is the high temperature shock on the concrete walls (due to liquid sodium, up to 850⁰C). Refining a previous crude formulation, a rational model for calculating moisture and heat transfer and pore pressures in concrete subjected to thermal shock is presented. In conclusion, a new design concept, in which the concrete vessel is completely dehydrated and kept hot throughout its service life in order to substantially improve its response to thermal shock as well as liquid sodium contact, is described. (Auth.)