Abstract: A pressure vessel susceptible to high temperatures, especially for containment of a nuclear-reactor core, is constituted of a cylindrical shell from a cast material such as cast steel, cast iron or concrete, and is prestressed by vertical cables which extend parallel to generatrices of the shell. Peripheral (circumferential) prestressing cables are provided around the shell which can be externally insulated. The peripheral tensioning cables are exposed externally of the insulation material and bear upon the shell of the vessel with heat-resistant elements of high compressive strength which extend through the external insulation.