This paper presents a one-dimensional analysis for the blast response of a sandwich beam/wide plate with a compressible core. The dynamic version of the recently developed extended high-order sandwich panel theory (EHSAPT) is first formulated. Material, geometric, and loading parameters are taken from blast experiments reported in literature. The novelty of EHSAPT is that it includes axial rigidity of the core and allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core and the rotation at the centroid of the core) instead of just one (shear stress in the core) of the earlier high-order sandwich panel theory (HSAPT). The solution procedure to determine the dynamic response to a general load applied on the top face sheet of a general asymmetric simply supported configuration is outlined. Although the dynamic EHSAPT is formulated in its full nonlinear version, the solution is for the linear problem so the accuracy of EHSAPT, along with the other theories, can be assessed by comparison to an available dynamic elasticity solution. Results show that the EHSAPT is very accurate and can capture the complex dynamic phenomena observed during the initial, transient phase of blast loading.