Abstract: Gas slippage and stress sensibility are two important factors which influence the development performances in shale gas reservoirs.To highlight their quantitative effects on gas production rates,a mathematical model with consideration of both slippage and stress sensibility in a two-phase flow in shale gas reservoirs was set up by using an equivalent porous media model, in which a finite difference method was used to solve the model. In addition, a numerical simulator of shale gas reservoirs was developed in Fortran(computer language).The effect of stress sensibility and gas slippage on gas well productivity was quantitatively studied by using the innovative simulator at a constant production rate and a specified bottom flow pressure in declining production.Numerical simulation results were then compared with field production data of Well W3 in a Haynesville shale gas reservoir.The numerical results showed that both formation pressure and permeability declined during depletion development of the gas reservoir and dramatical decline was observed near the wellbore region.In the first production year,shale gas production rate declined sharply;but slippage and stress sensibility displayed minor effect on the production rate.The effect of stress sensibility and gas slippage on production became more significant after 500 days of production.The decline curve closely tracked the simulation and history matching,and it thus validated the result calculated from a shale gas reservoir simulator with relatively high reliability.The successful development of a numerical simulator for shale gas reservoirs migth provide an innovative and effective approach for predicting gas production rates and decline curves.