Abstract: The analysis of the coupling mechanism of thermal-hydraulic-mechanical (THM) fields, and solid-liquid-gas (SLG) phases during gas extraction process is of profound significance to explore its numerical application in the gas occurrence regularity and its effective extraction radius. In this study, the Hudi coal mine in Qinshui basin is taken as the research area, the influencing factors of gas occurrence were analyzed, the differences in overburden load for gas pressure distribution and the factors influencing the effective extraction radius were further discussed by using the COMSOL software. The results show that the derivation of mathematical model in gas extraction shows that the process is a process the THM fields restrict each other, and the SLG phases influence each other. The longer the extraction time, the larger the influencing range of borehole, and the better the extraction effect. The larger the diameter of borehole, the larger the effective extraction radius, and the influence on gas extraction effect is smaller in the early stage and larger in the late stage. The borehole arrangement should be flexibly arranged according to the actual extraction situation. The higher the porosity, the higher the permeability, the better the gas extraction effect. The larger the overburden load of reservoir, the stronger the effective stress, which will result in the more severe the strain, and the closure of pore and fracture, which in turn will lead to the decrease of permeability and slow down the gas extraction. The relationship among extraction time, borehole diameter, negative pressure of gas extraction, permeability with effective extraction radius is exponential. This study has important theoretical and practical significance for clarifying and summarizing the gas occurrence regularity and its engineering practice.