The dynamics of the eyeball, most notably the changes in intraocular pressure, need to be stabilized optically to prevent noticeable changes in image quality. This control depends on the rheological properties of the eyeball coats and how the elasticity of the cornea, sclera, and limbus vary relative to one another. Nonlinear finite element modeling shows that image quality can be preserved over a range of elastic moduli. For intraocular pressure variations from 8 to 40 mm Hg, optical image stability is best for an elastic secant modulus of the cornea of 0.267 MPa. Optimal quality is achieved when the elastic moduli of the limbus and sclera are, respectively, 3.6 and 4 times that of the corneal modulus.