Purpose: We aimed to assess optic nerve head (ONH) deformations following acute intraocular pressure (IOP) elevations and horizontal eye movements (adduction and abduction) in control eyes, highly myopic (HM) eyes, HM eyes with glaucoma (HMG), and eyes with pathologic myopia alone (PM) or PM with staphyloma (PM+S). Methods: We studied 282 eyes, comprising of 99 controls, 51 HM, 35 HMG, 21 PM and 75 PM+S eyes. For each eye, we imaged the ONH using spectral-domain optical coherence tomography (OCT) under the following conditions: (1) primary gaze, (2) 20 degree adduction, (3) 20 degree abduction and (4) primary gaze with acute IOP elevation (to ~35 mmHg) achieved through ophthalmodynamometry. For each OCT volume, we automatically segmented the ONH tissues using deep learning. We performed digital volume correlation (DVC) analysis to compute IOP- and gaze-induced ONH displacements and effective strains (i.e. local deformations). All biomechanical quantities were compared across groups. Results: Under IOP elevation, we found that HM eyes exhibited significantly lower strains (3.9 +- 2.4 %) than PM eyes (6.9 +- 5.0%, p < 0.001), HMG eyes (4.7 +- 1.8%, p = 0.04) and PM+S eyes (7.0 +- 5.2%, p < 0.001). Under adduction, we found that HM eyes exhibited significantly lower strains (4.8% +- 2.7%) than PM+S eyes (6.0 +- 3.1%, p = 0.02). We also found significant associations between axial length (or refractive error) and strains - eyes with higher axial length and greater myopia were associated with higher strains. IOP-induced strains were also positively correlated with adduction-induced strains. Conclusion: We found that HMG eyes experienced significantly higher strains under IOP elevations as compared to HM eyes. Additionally, PM+S eyes experienced highest ONH strains as compared to other groups under all biomechanical loads. Our preliminary findings suggest the possibility of using a simple biomechanical test to tease out the susceptibility of HM eyes to further develop glaucoma and/or staphyloma.