This paper takes the containment structure as the research object, and carries out nonlinear finite element analysis by applying 0~2.5 times of design internal-pressure, the global nonlinear analysis on the 3D-solid containment model embedded with pre-stress tendons is performed under gravity and pre-stress loads. A prestressed containment structure model with complex spatial linear prestressed tendons is established precisely by using Concrete Damaged Plasticity (CDP) model and cooling method to simulate prestressed stress. In response to the failure predictions based on failure criteria, two phases of failure criteria in predicting the ultimate capacity of containment are proposed, including the functional failure and the structural failure. During the application of internal-pressure, the functional failure is determined by the damage degree of concrete, and the structural failure is determined by the yield of prestressed steel, providing a basis for the analysis and design of the containment structure.