This research is focused on development and enhancement of the model of fluid flow in a formation with stress-dependent permeability. Several typical axi-symmetrical problems of fluid flow in a multi-layered reservoir with account for wellbore storage and skin have been solved numerically. The permeability was assumed to be a function of the vertical deformation of the reservoir. This deformation is the result of changing stress-strain state in the elastic system, comprised of the reservoir itself and the surrounding rock mass. The change in the stress-strain state of the system is induced by pressure change in the layers of the reservoir. Numerical results qualitatively agree with observed field behavior. Such behavior includes (1) deviation of an inflow performance curve from the straight-line relationship at pressures above bubble-point pressure, (2) time- and rate-dependence of well-testing derivative, (3) asymmetry of processes of production and of injection, and (4) inconsistent results between drawdown and buildup, or injection and falloff tests. Based on the results, a procedure to estimate the parameters of the suggested permeability model is proposed.