The biomechanical environment within the optic nerve head, important in glaucoma, depends strongly on scleral biomechanical properties. Here we use a range of measured nonlinear scleral stress-strain relationships in a finite element (FE) model of the eye to compute the biomechanical environment in the optic nerve head at three levels of intraocular pressure (IOP). Three stress-strain relationships consistent with the 5th, 50th and 95th percentiles of measured human scleral stiffness were selected from a pool of 30 scleral samples taken from 10 eyes and implemented in a generic FE model of the eye using a hyperelastic five-parameter Mooney-Rivlin material model. Computed strains within optic nerve head tissues depended strongly on scleral properties, with most of this difference occurring between the compliant and median scenarios. Also, the magnitudes of strains were found to be substantial even at normal IOP (up to 5.25% in the lamina cribrosa at 15 mmHg), being larger than previously reported values even at normal levels of IOP. We conclude that scleras that are "weak", but still within the physiologic range, will result in appreciably increased optic nerve head strains and could represent a risk factor for glaucomatous optic neuropathy. Estimations of the deformation at the optic nerve head region, particularly at elevated IOP, should take into account the nonlinear nature of scleral stiffness.