The theory of sandwich construction developed in this paper proceeds from the simple assumption that the filling has only transverse direct and shear stiffnesses, corresponding to its functional requirements (§1). This supposition permits integration of the equilibrium equations for the filling (§2). The resulting integrals are used to study the compression buckling of a flat sandwich plate (§3). The formulae obtained are complex, but may be simplified in practical cases (§4). A second approach to sandwich problems is made in §5, where a theory of "bending" of plates is outlined. This generalises the usual theory, making allowance for flexibility in sheer. This approach is applied to overall compression buckling of a plate in §6, and agreement with the previous calculations is found. This suggests the possibility of calculating buckling loads for curved sandwich shells. A simple example, the symmetrical buckling of a circular cylinder in compression is worked out in §7. The theory developed would seem applicable to all cases of buckling of not too short a wave length (§8).