The paper deals with the problem of finding the optimal orientation of orthotropic properties for an elastic body, subjected to a plane state of stress, in order to maximize the stiffness of the body itself. A variational formulation of the problem is presented and the computation of the necessary condition for an optimal solution is carried out. The physical meaning of such a condition is then outlined, and its generality pointed out with reference to the case of two-dimensional flexural systems. Finally, an extension of the plane stress problem is formulated, taking into account as design variables both the orientation of orthotropy axes and the mechanical properties of the material, according to a global constraint on the structural cost.