The damage characteristics of the steel-Kevlar-steel structure are studied by nonlinear dynamics software. The whole destruction process of the sandwich structure is simulated. Moreover, the transmission and reflection of the shock wave in the structure are analyzed. It shows that the damage zone of the structure is just under the explosive. It is significantly different from the damage under non-contact explosion. The composite material has an effect on the spread of the shock wave, and effectively reduces the peak pressure. The sandwich structure has a good anti-impact performance. The results help to design and assess blast-resistant structures under contact explosion.