The prestressed containment structure is the last physical barrier against the spread of radioactive material. In addition to being able to resist the pressure caused by internal accidents, it should also have a certain ability to resist external projectiles or explosive shocks. Under the background of frequent terrorist incidents and intensified local conflicts, evaluating the performance of the containment structure under the close-in explosion of explosives carried by drones or light weapons is of great significance for maintaining the safety of nuclear power plants. In this paper, the CEL (Coupled Eulerian and Lagrangian) method is used to calculate the overpressure of the air blast, which is compared with the empirical formula. The test of the damage to the concrete slab under TNT near-in explosion reported in the literature is simulated, and the test results are compared. A numerical model of containment was established and calculated to predict damage behavior. The results show that the air overpressure simulated by the CEL method is in good agreement with the empirical formula, and the simulated results are consistent with the experimental results reported in the literature. Finally, predictions are made for the performance of the containment model under the close-in explosion. This method can be used to design or evaluate the performance of containment against close-in explosions.