Abstract: In over-cooling transient of reactors,the difference in temperature along the RPV wall will cause a large thermal stress,and then will generate a high tensile stress.Coupled with the internal big pressure,the defects in the inner surface of the RPV will propagate rapidly and even through the thickness.The probabilistic fracture mechanics theories were used in this paper.The uncertainty factors of the parameters were considered.The random numbers were generated using the Monte Carlo method on the basis of the random distribution of the parameters firstly,and then the limit function was established according to the fracture mechanics assessment criteria.Finally the failure probability was obtained by statistic calculation of the reliability data.