Glaucomatous optic neuropathy may be in part due to an altered biomechanical environment within the optic nerve head (ONH) produced by an elevated intraocular pressure (IOP). Previous work has characterized the magnitude of the IOP-induced deformation of ONH tissues but has not focused specifically on the mode of deformation (strain), i.e. whether the ONH tissues and cells are stretched, compressed or sheared. Circumstantial evidence indicates that the mode of deformation has biological consequences. Here we use computational models to study the different modes of deformation that occur in an ONH as a result of an increase in IOP. One generic and three individual-specific 3D models of the human ONH were reconstructed as previously described. Each model consisted of five tissue regions: pre and post-laminar neural tissue, lamina cribrosa, sclera and pia mater. Finite element methods were then used to predict the biomechanical response to changes in IOP. For each model we computed six local measures of strain, including the magnitude and direction of maximum stretching, maximum compression and maximum shearing strain. We compared the spatial and population distributions of the various measures of strain by using semi-quantitative (contour plots) and quantitative (histograms) methods. For all models, as IOP increased, the tissues of the ONH were subjected simultaneously to various modes of strain, including compression, extension and shearing. The highest magnitudes of all modes of strain occurred within the neural tissue regions. There were substantial differences in the magnitudes of the various modes of strain, with the largest strains being in compression, followed by shearing and finally by extension. The biomechanical response of an individual-specific ONH to changes in IOP is complex and cannot be fully captured by one measure of deformation. We predict that cells within the ONH are subjected to very different modes of deformation as IOP increases. The largest deformations are compressive, followed by shearing and stretching. Models of IOP-induced RGC damage need to be further refined by characterizing the cellular response to these different modes of strain.