Abstract: Hydraulic fracturing technology plays a key role in improving the recovery rate of shale gas. The improvement of permeability in relation to hydraulic fracturing depends on changes brought about by the proppant on the fracture structure in reservoirs. Then it is of great significance to describe the microscopic changes during this process by means of an accurate theoretical model. In this study, based on the heterogeneity of shale fracture and the compaction and embedment of a proppant, we proposed a permeability model to examine the combined effects of a proppant and stress to describe the change mechanism in permeability. Further, changes in fracture width and porosity were considered, and a calculation model of fracture compressibility under proppant compaction and embedment was proposed. The difference from previous studies is that the compressibility and permeability of supported fractures can be further quantified and analyzed by this model. Moreover, its rationality was verified by publicly released test data. The results show that, the compressive effect of stress and the embedding of proppant both have a negative impact on shale permeability.