Abstract: In order to study the coal permeability under three-dimensional stress condition,the permeability model of exponential form and cubic form were established. The two forms of permeability model were based on bundled match- stick concept. Meanwhile,the influence of matrix and fissure deformation of coal on permeability was analyzed by using the elastic theory. The two forms of model break through the uniaxial strain assumption and contain the fact that the transverse strain is not zero and the axial load is increased under three-dimensional stress condition. Under the condi- tions of changing axial pressure,confining pressure and gas pressure respectively,the theoretical model and laboratory test results were compared and analyzed. The results show that the coal permeability decreases with the increase of load level and the permeability increases with the increase of gas pressure. Under the two conditions,the coal permeability model of exponential form is better than the cubic form in the quantitative description of permeability evolution. The re- sults are of significance to the study of gas migration and extraction.