This study investigates the mechanical response of aluminum foam sandwich panels, sandwich cylindrical shells, and sandwich shallow shells under impact loads. First, a finite element model of the sandwich panel was established, and an impact load was applied. The numerical results were compared with theoretical and experimental results to verify the model's effectiveness. Second, the energy absorption efficiency and overall deformation of sandwich panels, sandwich cylindrical shells, and sandwich shallow shells under the same impact load were studied. The research shows that the energy absorption performance of the sandwich shells is better than that of the sandwich panels, and the overall deformation is less than that of the sandwich panels. The effect of increasing panel thickness on the two types of sandwich shell studies is based on this basis. The conclusions describe that increasing the panel thickness will significantly reduce the structure's energy absorption efficiency and deformation. Finally, the effect of single-and double-layer structure on the impact resistance of sandwich shells was studied when the total thickness of the sandwich structure was unchanged. The results show that compared with the single-layer structure, the energy absorption efficiency, overall deformation, and contact force between the projectile and structure of the double-layer structure will be reduced.