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Coalbed methane is not only a clean energy source, but also a major problem affecting the efficient production of coal mines. Hydraulic fracturing is an effective technology for enhancing the coal seam permeability to achieve the efficient extraction of methane. This study investigated the effect of a coal seam reservoir&rsquo, s geological factors on the initiation pressure and fracture propagation. Through theoretical analysis, a multi-layered coal seam initiation pressure calculation model was established based on the broken failure criterion of maximum tensile stress theory. Laboratory experiments were carried out to investigate the effects of the coal seam stress and coal seam dip angle on the crack initiation pressure and fracture propagation. The results reveal that the multi-layered coal seam hydraulic fracturing initiation pressure did not change with the coal seam inclination when the burial depth was the same. When the dip angle was the same, the initiation pressure linearly increased with the reservoir depth. A three-dimensional model was established to simulate the actual hydraulic fracturing crack propagation in multi-layered coal seams. The results reveal that the hydraulic crack propagated along the direction of the maximum principal stress and opened in the direction of the minimum principal stress. As the burial depth of the reservoir increased, the width of the hydraulic crack also increased. This study can provide the theoretical foundation for the effective implementation of hydraulic fracturing in multi-layered coal seams.