This chapter considers many of the same theoretical aspects of a sandwich panel as was presented in Chap. 7 . The principal difference resides with the transverse displacement representation for the core. In Chap. 7 , a linear or first-order power series was assumed for the transverse displacement function, whereas in the present case, a second-order polynomial is assumed for the transverse displacement thereby capturing the local and global instability modes on a higher order basis. Some of the theoretical considerations include the Kirchoff assumptions in the facings, a weak core, geometric imperfections, anisotropic laminated face sheets, and large displacements in the transverse direction. The governing equations are derived via an energy approach using Hamilton’s principle. The result is 11 equations of motion and nine boundary conditions prescribed along each edge. This is in comparison with 8 equations of motion and 8 prescribed boundary conditions required along each edge from the first theory (Chap. 7 ). At the conclusion of the chapter, an application of the buckling and postbuckling response is presented demonstrating how to apply and solve these theoretical equations.