Effective medium theories may be used for predicting the permeability and elastic properties of hydrocarbon reservoirs containing natural fractures, but need to be validated using numerical calculations. In this paper, three different types of stress boundary conditions are applied for a discrete fracture network (DFN) containing two sets of non-orthogonal vertical fractures. The variation of fracture aperture and compliance with stress is investigated, and the anisotropy in the effective permeability and seismic properties obtained from the simulations are compared with the predictions of effective medium theory. The nonlinear behavior of fractures observed in laboratory experiments is incorporated in the numerical method. Discrepancies between the permeability obtained from the simulations and from effective medium theory are attributed to an oversimplified treatment of fracture interconnectivity in the effective medium theory used. By contrast, the effective elastic compliances obtained from numerical simulation and effective medium theory are in good agreement, even for relatively complicated fracture networks. Although permeability anisotropy and seismic anisotropy both vary with stress, the relation between them is not simple.