Abstract: Shale gas mainly consists of two parts:the adsorbed and free state in shale formation with numerous microfractures.The accurate evaluation of the free gas in the fracture is very important for the early extraction of shale gas.Based on the material balance principle,Langmuir isotherm adsorption model,Bangham solid deformation theory,and the matrix system taken into consideration,the fracture system and the volume of adsorbed gas as the pressure changes,the material balance equation of shale gas is deduced.The equation is linearized to a straight line.The result shows that with the volume of adsorbed gas involved,the free gas in the matrix decreases,as well as the adsorbed gas decreases,while the free gas in the fracture systems increases,and the original gas in place decreases.The model is more realistic and the result is more accurate than it used to be.