A nuclear reactor is simplified and regarded as a pressure vessel to obtain its load-carrying capacity. Load-carrying capacity of a nuclear reactor is calculated by a finite element limit analysis considering work-hardening effect. The work-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 load-carrying 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.