The mathematical model describing the change of the stress-strain state of the sclera (the outer eye shell) after intravitreal injection is proposed. In the framework of the 3D theory of elasticity, the deformation of an orthotropic spherical layer is considered. Initially, the layer is subjected to the internal pressure. Then, the value of pressure required to increase the internal volume by a predetermined value is sought. The finite difference method implemented with the computing environment Maple^TM and finite element method in multipurpose software platform COMSOL Multiphysics (v. 5.0) are used to obtain the numerical solution. The impact of elastic moduli ratio (in meridional and circumferential directions) on the deformed configuration of the layer is examined. The calculations show that the initially spherical orthotropic spherical layer becomes ellipsoidal with increasing of the intraocular pressure (whereas the transversely isotropic layer remains spherical). The intraocular pressure values under injections of the additional volume of the uncompressed liquid are also obtained.