Changes in gas pressure or external stress cause changes in permeability; furthermore, the severity of stress disturbance in these situations can easily produce plastic yielding in the coal seam. Variations in coal seam permeability are also different between the elastic and plastic zones during the process of gas drainage. Therefore, it is necessary to consider gas pressure and external stress during pressure relief gas drainage in order to provide guidance for drilling in terms of location, timing, and pressure. An experimental study explored the relationship between external stress, gas pressure, and permeability in elastic and plastic fracture coal samples. This paper then conducts a numerical simulation of gas drainage according to the model, using the FISH programming language embedded in the FLAC3D numerical simulation software. The experimental results demonstrate that permeability in elastic coal samples first decreased and then increased with increasing gas pressure; in contrast, permeability in fractured coal samples decreased with increasing gas pressure and did not appear to increase at all within the tested gas pressure range. Decreases in permeability accompanied increases in gas pressure under constant effective stress; this indicates that decreases in effective stress lead to increases in permeability when the gas pressure exceeds the critical gas pressure under constant external stress. In contrast, when the gas pressure is less than the critical value, the Klinkenberg effect and matrix adsorption expansion play a major role in permeability changes. The influence of the Klinkenberg effect and adsorption on permeability decreases as gas pressure increases under the same effective stress or external stress conditions. Permeability and its sensitivity to gas pressure decrease with increasing effective stress or external stress. Meanwhile, the simulation demonstrates that permeability in the plastic zone increases in a nonlinear fashion as gas pressure decreases. These permeability increases can be divided into four stages: a rapid increase, gradual smoothing, a second slow increase, and ultimate stability.