The refractive index distribution of the geometry-invariant gradient refractive index lens (GIGL) model is derived as a function of Cartesian coordinates. The adjustable external geometry of the GIGL model aims to mimic the shape of the human and animal crystalline lens. The refractive index distribution is based on an adjustable power-law profile, which provides additional flexibility of the model. An analytical method for layer-by-layer finite ray tracing through the GIGL model is developed and used to calculate aberrations of the GIGL model. The result of the finite ray tracing aberrations of the GIGL model are compared to those obtained with paraxial ray tracing. The derived analytical expression for the refractive index distribution can be employed in the reconstruction processes of the eye using the conventional ray tracing methods. The layer-by-layer finite ray tracing approach would be an asset in ray tracing through a modified GIGL model, where the refractive index distribution cannot be described analytically. Using the layer-by-layer finite ray-tracing method, the potential of the GIGL model in representing continuous as well as shell-like layered structures is illustrated and the results for both cases are presented and analysed.