This paper is concerned with the optimum design for external reinforcement of a nuclear reactor pressure vessel(RPV) in a severe accident. During the severe reactor accident of molten core, the temperature and the pressure in the nuclear reactor rise to a certain level depending on the initial and subsequent condition of a severs accident. The reis of the temperature and the internal pressure cause deterioration of the load carrying capacity and could cause failure of the RPV lower head. The deterioration of failure can be mitigated by the external cooling or the reinforcement of the lower head with additional structures. While the external cooling forces the temperature of an RPV to drop to the desired level, the reinforcement of the lower head can attain both the increase of the load carrying capacity and the temperature drop. The reinforcement of the lower head can be optimized to have the maximum effect on the collapse pressure and the temperature at the inner wall. Optimization results are compared to both the result without the reinforcement and the result with the designated reinforcement.