Two non-classical theories for orthotropic plates of moderate thicknesses are discussed. In these theories both deformations, rotation and bending of the fibers and their elongations in the direction of the thickness of the shell are taken into account. The stress-strain state of a circular plate modeling the Lamina Cribrosa in the human eye is studied by means of these theories. Numerical results for displacements and stresses found with the presented theories are compared with those obtained with FEM.