A Finite Element implementation is presented to solve for Stokes flow on a deformable rock matrix reconstituted from a stack of computerized tomography images. Tightly coupling this flow solution with a mechanical deformation model exhibits the hydro-mechanical evolution of permeability in a fully saturated rock under compression. The scope of the presented micro-scale computation of permeability is demonstrated through a multi-scale simulation of pore pressure progression within a petroleum reservoir under production.