The dependency of permeability with depth, its sensitivity to injection pressure and earthquakes are all evidence that permeability depends on stress. Since stresses vary both vertically (lithostatic pressure) and horizontally (tectonic stresses) in the Earth’s crust, permeability is likely both depth dependent and anisotropic with potential consequences on flow that depend on the magnitude of the permeability variation with stress. In addition, the permeability is no longer a rock mass intrinsic property, but becomes a constitutive relationship between permeability and stress that we here refer to as “permecability”. The proposed analysis of the permeability dependency with stress is carried out for fractured rocks under conditions representative of deep storage of nuclear waste. It relies on a Discrete Fracture Network approach, where each fracture is assigned a stress dependent transmissivity. First, at single fracture scale, a literature review allows us to assume a simplified 3-parameter stress-transmissivity relationship, for which experiment based parameter estimates are available. At the network scale, each fracture experiences specific stress conditions that depend on the remote stress conditions, the fracture orientation and the stress fluctuations induced by surrounding fractures. Numerical simulations show that the latter cannot be neglected under the conditions under study, hence emphasizing the need to develop numerical methods able to both calculate the stress fluctuations in DFN models with hundreds of thousands of fractures of any size, and the DFN flow simulations to determine network scale equivalent permeabilities. We then analyze the relationship between the DFN structure, the stress-transmissivity relation, and the resulting permeability tensor. The anisotropy and magnitude of the permeability tensor highly depend on the intensity and directions of both fractures and remote stress. A complete sensitivity analysis is carried out to quantify this effect for a wide range of DFN models with varying hydraulic and mechanical (stiffness) parameters. Finally, we address the issue of defining as simply as possible the permecability constitutive relationship, which determines the rock mass permeability from DFN models and in-situ stress conditions.