Biological tissues have complex mechanical properties, which are deeply related to their function. It is thus needed to quantify the volumic displacements induced by mechanical load, rather than only surface displacements. In this article, we propose to use Optical Coherence Tomography as a simple and fast method to quantify the volumic deformation of the cornea under pressure. Indeed, the cornea plays a key role in vision, and any mechanical defect can impact the eye as it under the intraocular pressure. Our observations show that, in the tangential direction, the cornea's posterior part is softer than the anterior part. In the depth direction, we observed a strong compression, with depth-dependent heterogeneity, delineating three distinct regions. This strong compression can be explained only by important outward water fluxes. Our study shows the complexity of human corneal mechanics, highlighting the need of adequate volumic measure to characterize its strong anisotropy and depth-dependent behavior.