Stress analysis of tapered cylinder of reactor vessels is investigated by means of the intersection method. The tapered cylinder is approximated into three models-average cylinder, conical frustum, and ring. The results are compared with those of the finite element method program and an experiment. In this paper, the following results are obtained: (1) the best aproximation has been obtained by the ring model analysis: (2) the intersection analysis of the tapered cylinder by the ring model shows a sufficient accuracy for the stress analysis of reactor vessels.