The dynamic responses of end-clamped sandwich beams comprised of aluminum face sheets and close-celled aluminum foam cores are numerically simulated by loading the beams at mid-span. Three types of aluminum foam core having identical areal density are considered: homogeneous core, low-high gradient-density core, and high-low gradient-density core. Two-dimensional (2D) finite element (FE) models are created from tomographic images of the foam, which represent the cell shape and geometric distribution of real foams fabricated using the powder metallurgy foaming technique with blowing agents. To determine the mechanical properties of cell wall material, the numerically predicted uniaxial stress versus strain curve for homogeneous aluminum foam is fitted to that measured experimentally. The shock impulse is simulated using a uniformly distributed pressure versus time history. Depending upon the initial impulse applied, it is demonstrated that the deformation and deflection of the sandwich beam can be either bend or stretch dominated. Within the bend dominated domain, the foam-cored sandwich beams outperform monolithic solid beams of equal mass. However, the benefits diminish as the response of the sandwich becomes stretch dominated. Whilst the sandwich beam with homogeneous foam core shows the smallest mid-span deflection of its back facesheet, that with low-high gradient-density core achieves the largest average compressive strain and absorbs the most internal energy.