The report presents the development of rational methods of structural optimization for flat, corrugated core single truss core and web-core sandwich panels under two loading conditions in-plane shear loads, and combined uniaxial compression and in-plane shear loads. These methods provide a means by which minimum weight structures can be designed for a given load index, plate width, length, and face and core materials. The methods developed can be used as a means of rational material selection by comparing weights of optimum construction for various material systems as a function of applied load index. The methods are sufficiently general to account for orthotropic or isotropic face and core materials and various boundary conditions. Design procedures are given in detail for the design engineer to use.