The stress-strain state of one of the promising high-pressure apparatuses (HPA) after the assembly process and in the operating mode is investigated by the finite-element method. The stress state of plastically deformable container with a reactive mixture is calculated, and the effect of contact interaction and the elastoplastic deformations of equipment components is defined more precisely. The static and fatigue strengths of hard-alloy HPA components are estimated using previously developed criteria. The dependence of the strength and longevity of geometrically similar dies and punches on their effective volume is established. An interpretation of the most characteristic forms of HPA is given on the basis of computational results, and several means of improving their designs are indicated.