To discover the mechanism of underground dynamic disasters close to thrust faults of an arc fault plane, a simplified mechanical model of arc fault planes under the influence of horizontal tectonic stress is constructed. The distribution laws of both horizontal tectonic stress and additional vertical stress induced by the tectonic stress are acquired, and then a mathematical model of the critical angle of thrust-shear slide of hanging wall is set up. The study results show that both horizontal tectonic stress and additional vertical stress increase with the increase of a fault dip. When the dip angle is close to 90°, the additional vertical stress increases rapidly, and its maximum is several times higher than the tectonic stress. The critical angle of the fault thrust sliding is calculated based on mechanical analysis, and this is hoped to provide some reference for the early warning dynamic disasters about coal and rock.