The 3D problem of deformation of the elastic orthotropic spherical layer under normal pressure applied on the outer and inner surfaces is analyzed. The asymptotic solutions of the first approximation are obtained for a slightly orthotropic layer, i. e. for which the values of elastic moduli in meridional and circumferential directions are close. The obtained solutions are used in analysis of the scleral shell under intraocular pressure and may also be used in solution of the inverse problem, i. e. in analysis of the stress-strain state of a human eye under injection. The influence of elastic modulus in meridional and circumferential directions on the change of the relative layer thickness under normal pressure and length change of the anteroposterior axis of the eye due to an increase in intraocular pressure is studied. Refs 9. Figs 3.