This work presents results from numerical simulations of optic nerve head's (ONH) biomechanical behavior during exposure to elevated intraocular (IOP) and/or intracranial pressure (ICP) for ocular hypertension conditions. At the same time, a range of geometric and material properties of the eye structure and their interrelation with elevated IOP and ICP values are investigated. These simulations are performed on a generic model of the eye, which allows parametrical modification of geometric and material properties. Our main interest is in measuring ONH's potential damage in ocular hypertension due to intracranial pressure. Simulation results indicate a significant role of ICP in post-laminar neural tissue failure and a possible role of central corneal thickness (CCT) and scleral modulus in clinical assessment and treatment of patients with ocular hypertension (OHT). Specifically, CCT was found to affect ONH at early stages of damage in ocular hypertension conditions, and high scleral modulus seems to result in reduced shear failure in lamina cribrosa in a similar OHT state. These findings suggest that CCT could be a risk factor for glaucoma in OHT patients at initial stage along with cornea stiffness. Graphical abstract Graphical abstract.