An analytical method is proposed to study the local and global instability of three-layered assymmetric sandwich beams with arbitrary relative face thicknesses ranging from very thin faces to a vanishing core height. The method accounts for extensional orthotropy, shear elasticity, Poisson’s ratio effects and lateral compressibility within each layer. As each layer is modelled in an identical manner and all stress and displacement related interface conditions are satisfied, there is no limitation with regard to geometry relations, except for numerical instabilities or convergence criteria. The displacement functions are represented by Fourier series which leads to a set of 12 linear equations for each value of the harmonic m The eigenfunction associated with the minimum load will then represent the (local or global) design buckling (or wrinkling) mode.
The results can be compared with buckling formulas like that proposed by Hoff  or the formula related to a beam on elastic foundation , as well as the approximation for Euler columns accounting for shear elasticity. It becomes evident that modifications to the aproximate methods may be suitable for some geometric relations and material properties.