Optimum laminate configurations for laminated rectangular plates under uniaxial or biaxial compression are investigated and are obtained under buckling constraints. Complete freedom is permitted in the selection of the ply angle variation through the thickness; however, it is proved that the maximum buckling load occurs when the orientation angle in each of the layers is the same. Three types of optimal angle (direction) are obtained in terms of the material properties, the geometrical properties and the type of buckling mode. They are expressed in closed analytical form.