In this work, the biomechanical responses of the optic nerve head (ONH) to acute elevations in intracranial pressure (ICP) were systematically investigated through numerical modeling. An orthogonal experimental design was developed to quantify the influence of ten input factors that govern the anatomy and material properties of the ONH on the peak maximum principal strain (MPS) in the lamina cribrosa (LC) and postlaminar neural tissue (PLNT). Results showed that the sensitivity of ONH responses to various input factors was region-specific. In the LC, the peak MPS was most strongly dependent on the sclera thickness, LC modulus, and scleral canal size, whereas in the PLNT, the peak MPS was more sensitive to the scleral canal size, neural tissue modulus, and pia mater modulus. The enforcement of clinically relevant ICP in the retro-orbital subarachnoid space influenced the sensitivity analysis. It also induced much larger strains in the PLNT than in the LC. Moreover, acute elevation of ICP leads to dramatic strain distribution changes in the PLNT, but had minimal impact on the LC. This work could help to better understand patient-specific responses, to provide guidance on biomechanical factors resulting in optic nerve diseases, such as glaucoma, papilledema, and ischemic optic neuropathy, and to illuminate the possibilities for exploiting their potential to treat and prevent ONH diseases.