This paper presents the application of a computational homogenization technique to examine the stress-induced permeability evolution in a quasi-brittle material susceptible to damage. The concepts involved in the constitutive modeling and the computational procedures are summarized. The developments are applied to investigate the response of the model in simulating experimental investigations of permeability evolution in a granitic rock. The influence of both the isotropic and the deviatoric stress states on the evolution of the spatially averaged permeability is derived from the computational simulations and is compared with experimental observations. It is shown that with the provision of supplemental material parameters the computational approach is able to satisfactorily match the experimental results.