Abstract: In order to clarify the effective extraction range of gas drainage boreholes in steeply inclined coal seams and reasonably arrange the locations of drainage boreholes, taking Wudong Coal Mine No.43 coal seam as an example, and numerical simulations were used to obtain the effective drainage range of gas drainage holes in steeply inclined coal seams. According to the law of time change, the gas percolation unit model around the steeply inclined coal seam was established, the mathematical model of the effective drainage range of the steeply inclined coal seam was deduced, and the numerical simulation and mathematical model were verified by the field measurement results, and the average relative error rate was small (both are less than 5%). Numerical simulation results show that: compared with the effective gas drainage range of conventional coal seam boreholes, the effective drainage distance and drainage time of steep coal seams have a non-linear relationship; during the drainage process, the effective drainage range increases with time. The expansion speed is different in different directions of the borehole plane, and the effective drainage area becomes an elliptical area after finally stabilizing. Through the analysis of the force state on the coal wall around the boreholes in steeply inclined coal seams, it is believed that the main reason for the difference in the effective extraction range is that the emergence of the boreholes has changed the original distribution of ground stress, and the stability of the coal wall around the drilling was impaired, the physical and mechanical properties of the coal in a certain range nearby change.In addition, the redistribution of ground stress also has a certain impact on the permeability of the coal seam around the borehole. In order to quantitatively study the development trend of the effective drainage range on the two-dimensional section perpendicular to the borehole with time, the mathematical model of the effective extraction range of the steep coal seam was used to obtain the expression of the effective extraction range of the steep coal seam, and the extraction in different directions was analyzed. The degree of difference caused by the expansion speed has a certain guiding effect on the field application of gas drainage boreholes in steeply inclined coal seams.