The transient blast response of a sandwich panel that consists of a compressible core with in-plane rigidity using the extended high-order sandwich panel theory is presented and compared with elasticity closed-form solutions. The mathematical formulation of the extended high-order sandwich panel theory for the transient dynamic response of sandwich plates is described along with a numerical investigation. The extended high-order sandwich panel theory formulation takes into account the shear resistance of the core and its compressibility, which is envisaged through nonidentical displacements of the upper and the lower facesheets and its in-plane rigidity. The equations of motion and the appropriate boundary conditions are derived using the Hamilton’s principle. A numerical investigation is conducted on a simply supported sandwich panel, and its results are compared with a benchmark elasticity closed-form solution. The results include deformed shapes at the first millisecond at various time steps; displacements of the various constituents, as well as various stress resultants in the facesheets; and stress distributions within the core and at its interfaces with the facesheets. The extended high-order sandwich panel theory and the elasticity benchmark results correlate very well. Finally, a summary is presented and conclusions are drawn.