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The buried depth of coal seams in China gradually increases as shallow resources decrease. The purpose of this article is to reveal the effect of buried depth on gas extraction boreholes. Firstly, we analyzed the shortcomings of the Mohr–Coulomb (M-C) constitutive model for simulating excavation problems and introduced the strain-softening (S-S) model and its advantages. Subsequently, we constructed the gas extraction models with different buried depths based on the S-S model and combined them with the evolution equations for permeability and the equations for gas migration. Then, we studied the difference between the M-C and S-S models using numerical simulations. We found that the influence of the S-S phenomenon in the surrounding rock of boreholes is more significant as the buried depth increases—that is, the strain-softening has a significant buried depth effect. When the buried depths were 300, 500, and 700 m, the maximum ratios of permeability to the initial permeability obtained from the Mohr–Coulomb model were 1.37, 6.88, and 97.56, respectively; the maximum ratios of permeability to the initial permeability obtained from the strain-softening model were 2.06, 291.23, and 3629.66. The differences in the increase zone of permeability from the two models also increased with the increase in the buried depth. The distribution curves of gas pressure in the surrounding rock of boreholes obtained from the S-S model were below those of the M-C constitutive model at the same buried depth, and the zones with slowly increasing gas pressure with the increase in buried depth were more obvious in the S-S model compared with the M-C constitutive model. The differences in borehole effective extraction radius also increased gradually between the S-S and M-C models as the buried depth increased. Through the analysis of the research results, we found that S-S of the surrounding rock has a lesser influence on the gas extraction boreholes, and the S-S phenomenon in the surrounding rock of boreholes can be ignored when the buried depth is relatively shallow. It is increasingly necessary to consider the S-S phenomenon in the surrounding rock of boreholes with the gradual increase in the buried depth.