The pore network in shale reservoirs comprise of nanoporous organic matter (OM) and micron-size pores in inorganic material (iOM). Accurate gas transport models in shale must include gas slippage, Knudsen diffusion, surface diffusion, and sorption. The change in pore size due to the applied stress could consequently affect gas transport processes. In this study we a compression coefficient to characterize the influence of stress sensitivity on key parameters for gas transport. We consider separate stress response in nanoporous organic matter and iOM because of their different mechanical properties. The effects of compressibility on apparent permeability of OM and iOM are analyzed at different pore sizes, pore pressures and for different gas compositions. Our results show that compressibility has a greater influence on the apparent permeability of iOM than on OM when pore sizes are smaller than 10 nm, whereas compression has similar impact on apparent permeability of both media when pore sizes are larger than 10 nm. With the same effective stress, lower pore pressure results in greater impair in permeability. We conducted a reservoir simulation study using conventional dual-continua model with our developed pressure dependent porosity and permeability to showcase field implication of this study. This work is an important and timely investigation of the development of shale-reservoir-flow simulators. (C) 2017 Elsevier Ltd. All rights reserved.