We do not yet have definitive data on the optical structure of the lens, including surface shapes and gradient refractive index distribution. Some data do exist but we need much more data to complete our knowledge of this structure. However, using current and sparse knowledge, we can use mathematical modelling to study the effects of surface shapes and gradient refractive index structure on the Gaussian and aberration properties of the lens. The equations extracted from this modelling show some interesting results, for example, the way the gradient index structure provides some of the refractive power and how this structure possibly predicts a negative spherical aberration of the lens, which is observed in real eyes. This modelling will provide a firm theoretical foundation for analysing more accurate and extensive lenticular shape and refractive index data as they become available.