In this paper a new method for the determination of flexural rigidities in orthotropic plate bending problems is presented. Boundary integral equations are established for the curvatures and the deflections inside the domain. By a simple discretization of the boundary and the inside plate, the elimination of curvatures is possible. If the fundamental solution of isotropic plates is chosen, then a linear system of n equations with three unknowns is obtained. These equations are provided by the knowledge of the deflections inside the plates, and the unknowns are the flexural rigidities. By using the least square method, the computation of these rigidities becomes easy.