The objective of this study was to evaluate which hyperelastic model could best describe the non-linear mechanical behavior of the cornea, in order to characterize the capability of the non-linear model parameters to discriminate structural changes in a damaged cornea. Porcine corneas were used, establishing two different groups: control (non-treated) and NaOH-treated (damaged) corneas (n = 8). NaOH causes a chemical burn to the corneal tissue, simulating a disease associated to structural damage of the stromal layer. Quasi-static uniaxial tensile tests were performed in nasal-temporal direction immediately after preparing corneal strips from the two groups. Three non-linear hyperelastic models (i.e. Hamilton-Zabolotskaya model, Ogden model and Mooney-Rivlin model) were fitted to the stress-strain curves obtained in the tensile tests and statistically compared. The corneas from the two groups showed a non-linear mechanical behavior that was best described by the Hamilton-Zabolotskaya model, obtaining the highest coefficient of determination (R > 0.95). Moreover, Hamilton-Zabolotskaya model showed the highest discriminative capability of the non-linear model parameter (Parameter A) for the tissue structural changes between the two sample groups (p = 0.0005). The present work determines the best hyperelastic model with the highest discriminative capability in description of the non-linear mechanical behavior of the cornea.