Summary: This paper is concerned with the structural optimization problem of maximizing the shear buckling load of rectangular plates for a given volume of material. Optimality conditions are first derived via variational calculus, and a double cosine thickness varying plate and a hybrid double sine thickness varying plate are then finely tuned in a one-parameter optimization search using a home coded program for an analysis that utilizes the Rayleigh-Ritz method until convergence. Results indicate an increase of \(33\%\) in capacity for an orthotropic plate having \(50\%\) of the fibres in the \(0^\circ\) direction and the other \(50\%\) in the \(90^\circ\) direction.