The influence of bending-extension coupling and comparatively low transverse shear stiffness on the stability of unsymmetric laminated plates makes it necessary to consider these effects in the structural analysis. The discrete plate analysis is one way to describe the local stability of sectional plane struc- tural components [1]. In this analysis, the individual segments are considered as plates with rotational restraints that represent the supporting effect of the surrounding structure, so that the local stability of the entire structure can be calculated. This work is about the analytical description of the mentioned laminated plates with elastic restraints. The existing L ́evy’s solutions for example from [2] have been further developed for this purpose. The presented L ́evy’s solutions for the buckling load provide an exact solution for symmetric and unsym- metric cross-ply laminates as well as antisymmetric angle-ply laminates in the framework of the theory. The influence of shear deformation is shown by considering Classical Laminated Plate Theory (CLPT), First-Order Shear Deformation Theory (FSDT), and Third-Order Shear Deformation Theory (TSDT). The new formulation of the rotational elastic restraints in the framework of the TSDT shows an influence on the twisting and warping of the plate cross-section. This study shows the influence of bending-extension coupling on different fibre angles and layer se- quences. The role of shear deformation on different laminated plate theories regarding the stability of unsymmetrically laminated plates under different boundary conditions is discussed