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The rock burst caused by geological structures is abrupt and destructive, and the special structure of a graben fault decides the uniqueness of mine ground pressure in the mining process. By simplifying the graben fault structure, the evolution law of roof stress during the recovery process was studied based on the theory of the elastic shear beam. The change laws of stress field and displacement nearby the fault during the advancement process of the working face were explored through a numerical simulation, and the instability mechanism and laws of rock strata nearby this graben fault were revealed. This study will be of great significance for preventing and controlling the rock burst in the graben fault.