Glaucoma is the leading cause of irreversible blindness and is characterized by the death of retinal ganglion cells, which carry vision information from the retina to the brain. Although it is well accepted that biomechanics is an important part of the glaucomatous disease process, the mechanisms by which biomechanical insult, usually due to elevated intraocular pressure (IOP), leads to retinal ganglion cell death are not understood. Rat models of glaucoma afford an opportunity for learning more about these mechanisms, but the biomechanics of the rat optic nerve head (ONH), a primary region of damage in glaucoma, are only just beginning to be characterized. In a previous study, we built finite-element models with individual-specific rat ONH geometries. Here, we developed a parametrized model of the rat ONH and used it to perform a sensitivity study to determine the influence that six geometric parameters and 13 tissue material properties have on rat optic nerve biomechanical strains due to IOP elevation. Strain magnitudes and patterns in the parametrized model generally matched those from individual-specific models, suggesting that the parametrized model sufficiently approximated rat ONH anatomy. Similar to previous studies in human eyes, we found that scleral properties were highly influential: the six parameters with highest influence on optic nerve strains were optic nerve stiffness, IOP, scleral thickness, the degree of alignment of scleral collagen fibres, scleral ground substance stiffness and the scleral collagen fibre uncrimping coefficient. We conclude that a parametrized modelling strategy is an efficient approach that allows insight into rat ONH biomechanics. Further, scleral properties are important influences on rat ONH biomechanics, and additional efforts should be made to better characterize rat scleral collagen fibre organization.