The object of this work has been to develop a mechanical and numerical model of the eye submitted to vibrations, and in particular, to calculate the influence of intraocular pressure (IOP) on the eye resonance frequencies. Our mechanical model of the eye relies upon the theory of the mechanics of continuous media. The numerical model results from a modal analysis of the vibrations of the eye using a finite element method (FEM) for discretization. The eye can be schematically represented as a prestressed shell, filled by an inviscid barotropic compressible fluid, which leads us to formulate and solve a problem of vibrations of a coupled fluid-structure system. The corneoscleral shell has been modeled as a thin and thick shell, taking into account material nonlinearities in the thick case. Numerical results obtained for the attached eye demonstrate a fair sensitivity of the resonance frequencies to the variations of the IOP; thus, founding the interest of the surveillance of the resonance frequency of the eye.