The mechanophysiology of tissues in the posterior eye have been implicated for diseases such as myopia and glaucoma. For example, the eye-globe shape, and consequently optical axial length, can be affected by scleral stiffness. In glaucoma, an elevated intraocular pressure is the primary risk factor for glaucoma, which is the 2nd most prevalent known cause of blindness. Recent work has shown that biomechanical properties of the optic nerve are critical for the onset and progression of glaucoma because weak tissues cause large displacements in the optic nerve, causing tissue damage. In this work, we utilize air-pulse optical coherence elastography (OCE) to quantify the spatial distribution of biomechanical properties of the optic nerve, its surrounding tissues, and the posterior sclera. Air-pulse measurements were made in a grid on in situ porcine eyes in the whole eye-globe configuration as various IOPs. The OCE-measured displacement process was linked to tissue stiffness by a simple kinematic equation. The results show that the optic nerve and peripapillary sclera are much stiffer than the surrounding sclera, and the stiffness of the optic nerve and peripapillary sclera increased as a function of IOP. However, the stiffness of the surrounding sclera did not dramatically increase. Our results show that understanding the dynamics of the biomechanical properties of the eye are critical to understand the aforementioned diseases and may provide additional information for assessing visual health and integrity.