Abstract: The critical fracture criterion of a cylinder with V-notches on the inner surface under explosive loading is studied. The functional expression of relationship between stress concentration factor and non-dimensional geometrical structure parameters is fitted through results of a series of calculation models using the numerical simulation method. The damage evolution equation is modified on the base of Feng jia-bos study given the stress-strain field at the root of V-notch effected on the accelerating growth of holes or cracks. Assuming the natural expansion rate of the cylinder to be constant, the critical fracture criterion of the cylinder with notches on the inner surface is obtained. Results of theoretical analysis and the experimental results are consistent with each other.