In order to ensure the safety of the incineration process， the incinerator must be able to withstand the impact of accidental explosion when the waste energetic materials are incinerated. The dynamic coefficient method and the method proposed by Atomic Weapons Establishment （AWE Method） were used to design the shell of vertical incinerator for waste energetic materials. Then， three-dimensional numerical simulation of the shell stress of the designed incinerator under detonation of energetic materials was carried out using AUTODYN software. The influence of exhaust gas outlet， outlet position and detonation position of energetic materials on the anti-explosion performance of the incinerator was analyzed. Numerical simulation results show that the existence of the outlet destroys the continuity of the shell， therefore， the stress concentration occurs near the outlet， and the maximal stress appears at the upper edge of the outlet. Besides， as the diameter of the outlet increases， as the center of the outlet is closer to the shell cover， and as the detonation position of energetic materials is closer to the outlet， the stress concentration at the upper edge of the outlet becomes more serious. When the energetic material is close to the incinerator shell， the explosion will cause plastic deformation of the shell. Hence， when the diameter of outlet is determined， some measures can be taken to ensure the safety of the incineration process， such as keeping the outlet away from the seal plate， setting a stiffening ring at the outlet and keeping a certain distance between energetic materials and the shell.