Upon the completion of experimental investigations and theoretical researches by Zheng, Deng and Chen, et al.，the damage mechanism and failure modes of discrete multi-layered explosion containment vessels(DMV) are classified and discussed in this paper. Three failure modes are considered including tensile failure mode, shear failure mode and adiabatic shearing fracture. The different failure criteria are proposed according to these failure modes. Combining the thermo-viscoplastic constitutive law and the proposed failure criteria, the numerical failure analysis is performed to describe the transient failure procedure of vessels under the internal explosive loading, and failure assessment is applied to determine the critical crack size. The numerical result also shows that the tensile failure mode is applicable for general plastic deformation, which is not conservative enough to deal with local material damage and crack propagation. And the rate-dependent critical corresponding to adiabatic shearing fracture is more suitable to the crack propagation especially for the structure under severe explosive loading. The recognition is helpful to establish the design method of DMV