Summary: Consider a composite sandwich plate with balanced or unbalanced anisotropic composite laminated faces and an ideally orthotropic core. A closed-form solution of the buckling load is derived for the composite sandwich plates consisting of cross-ply symmetric laminate faces with all edges simply supported. In addition, a general scheme is developed for the composite sandwich plates with arbitrary sandwich layups, boundary and loading conditions. By combining the present buckling analysis with Powell's conjugate direction method, an optimal algorithm is established to find the optimal sandwich layup in resisting biaxial compression, as well as in-plane shear loads.