Purpose The elastic moduli of the cornea, sclera, and limbus for different corneal eccentricities (e) and varying levels of intraocular pressure (IOP) were modelled in order to determine how the rheological properties, especially those of the limbus, need to alter to maintain optical image quality when the eye is subjected to small variations in IOP. Methods Finite element analysis (FEA) was used to construct eyeball models with four different corneal eccentricities (e = 0, 0.33, 0.5, 0.65). Three values for Young's modulus of the cornea were tested in all models (0.2 megapascal (MPa), 1.2 and 10 MPa). For each corneal modulus, scleral moduli of 3, 4, 5, 7, and 10 times that of the corneal modulus were selected. The limbal modulus was varied to optimise image quality of the eye model subjected to IOP variations of +/- 0.8 mmHg for three different levels of IOP (8, 16, and 32 mmHg). Results The elastic modulus of the limbal ring increases with an increase in corneal modulus and rises to a peak when the ratio of scleral to corneal moduli is between 5 and 7 depending on corneal eccentricity. Different levels of IOP produce only slight differences in the relative moduli required to maintain optical image quality. Conclusions The significance of a peak in the value of Young's modulus of the limbus is not clear but suggests that there may be an optimal limbal modulus that must be balanced with the moduli of cornea and sclera for preservation of image quality.