Abstract: Fluid flow in hydrocarbon and low permeability reservoirs is traditionally analyzed by assuming that the formation permeability is constant.However,the assumption can result in significant errors in the estimation of temporal and spatial variation of pressures when the formation permeability is pressure sensitive.The transient pressure response of a double porosity and double permeability media that is stress-sensitive is studied.Not only the double permeability feature of oil reservoir but also the deformation of medium in stress-sensitive reservoir is considered,and the mathematical model of the deformation double porosity/double permeability medium is constructed.The dependence of permeability on pore pressure makes the flow equation strongly nonlinear.The numerical solution of a constant-rate production of a finite radius well is obtained by the Douglas-Jones predictor-corrector in an infinitely large system.The change rule of pressure is discussed when the parameters of double porous medium and the parameters of deformation change.The plots of typical pressure variation are given in a few cases,and an application example of the proposed method is also given.