Biomechanical factors acting within the optic nerve head (ONH) likely play a role in the loss of vision that occurs in glaucoma. In a companion paper (Sigal et al. 2008), we quantified the biomechanical environment within individual-specific ONH models reconstructed from human post mortem eyes. Our goal in this manuscript was to use finite element modeling to investigate the influence of tissue material properties on ONH biomechanics in these same individual-specific models. A sensitivity analysis was carried out by simulating the effects of changing intraocular pressure on ONH biomechanics as tissue mechanical properties were systematically varied over ranges reported in the literature. This procedure was repeated for each individual-specific model described in the companion paper (Sigal et al. 2008). The outcome measures of the analysis were first and third principal strains, as well as the derived quantity of maximum shear strain, in ONH tissues. Scleral stiffness had by far the largest influence in ONH biomechanics, and this result was remarkably consistent across ONH models. The stiffnesses of the lamina cribrosa and pia mater were also influential. These results are consistent with those obtained using generic ONH models. The compressibility of the pre-laminar neural tissue influenced compressive and shearing strains. Overall, tissue material properties had a much greater influence on ONH biomechanics than did tissue geometry, as assessed by comparing results between our individual-specific models. Material properties of ONH tissues, particularly of the peripapillary sclera, play a dominant role in the mechanical response of an ONH to acute changes in IOP and may be important in the pathogenesis of glaucoma. We need to better understand inter-individual differences in scleral biomechanical properties and whether they are clinically important.