Load-carrying capacity of pressure vessels is studied by finite element limit analysis. The finite element limit analysis consists of a limit formulation, finite dimensional approximation and a minimization technique based on a variational principle of duality. In this study, a nuclear reactor is simplified and regarded as a pressure vessel to obtain its load-carrying capacity. The collapse load of a nuclear reactor is calculated by a finite element limit analysis considering strain-hardening effect. The strain-hardening effect generally enhances the safety margin of a pressure vessel from the incipient yielding to the rupture. In the calculation, the wall thickness of a nuclear reactor is altered as a design parameter to identify the validity of the current design. The current design proves to be a good design in the sense of a pressure vessel from the numerical result. The numerical result provides the collapse loads capacity and collapse modes of a nuclear reactor with the variation of the wall-thickness and demonstrates the capability of the present method for the optimum design of a pressure vessel. In addition, to study the thermal effect load-carrying capacity of pressure vessels, the collapse load of a nuclear reactor is calculated with the elevation of temperature in a reactor vessel. The nuclear reactor is assumed to undergo a severe accident with fuel cores melting. The situation is simply described by various thermal boundary conditions. The numerical result demonstrates variation of the collapse load and collapse mode of a nuclear reactor with various boundary conditions assumed.