A two-dimensional finite element model (FEM) of an eye consisting of two spherical layers loaded with intraocular pressure is presented. The upper corneal layer is considered to have a rigid elastic annular insertion. The model is used to analyze St Petersburg the changes in stress-strain state of the eyeball after corneal ring implantation for patients with high degree myopia and thin cornea. FE simulation is performed in the ANSYS software package. The Yeoh, neo-Hookean and 2-parameter Mooney-Rivlin hyperelastic models are used to describe the nonlinear properties of the cornea. The effect of these models on the change in corneal radius of curvature in response to ring insertion is evaluated. The computational results show that the hyperelastic models provide corneal deformations after MyoRing treatment of the same order of magnitude as in clinical practice.