Although it has been reported that the gas flow in the cleat system may be of the non-Darcy nature, little has been known on how this non-Darcy flow affects the coal seam gas (CSG) extraction. One of the major reasons is that prior studies on this subject have not included the impact of gas sorption-induced coal deformation (swelling or shrinking) and the nature of two extremely different time scales between processes in the coal matrix and ones in the cleat system. In this study, a fully coupled finite element (FE) model of coal deformation (gas sorption induced swelling or shrinking), non-Darcy flow in fractures and gas diffusion in coal matrix is developed to quantify these non-Darcy flow effects. The fully coupled model can include EDM (Equilibrium Desorption Model) or DDM (Dynamic Desorption Model). In EDM, the gas sorption in the matrix system is a function of gas pressure only, i.e., the sorption process completes instantly when the cleat pressure changes. In DDM, the gas sorption in the matrix system is a function of both gas pressure in the cleat and the diffusion time in the matrix, i.e., a time lag between the cleat flow and diffusion process in the matrix exists. When only Darcy flow is assumed, this model was verified against both the model results of a vertical gas well performance by using ECLIPSE and field data from the Horseshoe Canyon coalbed gas well. Both EDM and DDM are applied to quantify the relationship among non-Darcy effect, production parameters, diffusion times, and coal seam compaction. Model results indicate that the non-Darcy effect is significant for high pressure drops and exists only within a small region near wellbore and that different diffusion times may produce two peaks of production rate, one is due to gas flow in the cleat system at the early stage and the other is due to gas diffusion at the late stage. The coal seam compaction can reduce the production rate much more than the non-Darcy flow effect at the early stage but has slightly impact at the late stage. (C) 2012 Elsevier B.V. All rights reserved.