The three-dimensional state equations for the initial buckling of orthotropic thick plates are established in the Cartesian co-ordinate system in this paper without imposing any assumptions about the displacement models or stress distribution across the thickness of the cross-section. By using the continuity conditions of the displacement and stresses on each interface between any two adjacent layers, the state equations for the laminates, which consist of orthotropic layers, were obtained. A unified exact solution for the buckling of simply supported rectangular laminates with any given number of orthotropic layers is presented in the paper by means of the well-known Cayley-Hamilton theorem. All the equations of elasticity can be satisfied exactly and the nine elasticity constants of orthotropy for each layer are fully taken into account. Regardless of the number of the layers considered, only a set of simultaneous linear algebraic equations of 3rd order needs to be solved in the final stage of the solution. The numerical results were calculated and compared with those of thin plate theory, Mindlin analysis and those due to Srinivas et al. who also solved the problems with the three-dimensional theory of elasticity.