Abstract: Mastering the characteristics of permeability and formation fracture pressure in the pressure-relief coal seam under a goaf is the basis and premise for achieving the safe and efficient development of coalbed methane resources in such areas. Taking the East Fifth Panel of the Sihe Coal Mine in Shanxi Province as an example, and combined with the mining geological conditions, the numerical method is used to analyze the stress, vertical and horizontal permeability changes, and floor failure characteristics of the underlying strata under the goaf of the No. 3 coal seam. Based on the Griffith energy theory, a calculation model for formation fracture pressure is constructed, and the maximum fracture pressure of the underlying strata under the goaf is predicted. The results show that, with the mining of the No. 3 coal seam, the failure depth of the floor is approximately 20 m, and the mining-induced fractures in the floor are predominantly bedding fractures. The underlying strata beneath the goaf exhibit distinct characteristics of pressure relief and enhanced permeability. Without considering the re-compaction of the goaf, the vertical pressure relief coefficient of the No. 9 coal seam, located 50 m below the goaf, can reach up to 40%. Significant differences are observed between the horizontal and vertical permeability changes in the No. 9 coal seam: horizontal permeability increases by approximately 170 times, while vertical permeability increases by about 3.4 times. The maximum increase in horizontal permeability of the underlying strata in the goaf is 260 times, and the maximum increase in vertical permeability is 15 times. Due to the influence of mining, the stress mechanism in the underlying strata of the No. 3 coal seam transitions into a reverse fault stress mechanism. The fracture pressure for hydraulic fracturing in the No. 9 coal seam is 18 MPa, whereas the formation fracture pressure for hydraulic fractures communicating with the goaf is 36 MPa. The maximum fracturing pressure should be controlled below 36 MPa to prevent hydraulic fractures from connecting with the goaf, which could lead to coalbed methane leakage from the No. 9 coal seam into the No. 3 coal seam goaf, resulting in gas well failure. These findings provide valuable insights for ensuring the safe and efficient development of coalbed methane in Goaf regions.