In order to study the instability mechanism of the pressure-arch in the mining field under different dip angles of the coal seam, the structure mechanics model of the pressure-arch in the mining field was built based on a practical engineering. The moment, shear, and axial force at any section of the pressure-arch axis are obtained through the pressure-arch axis equation. It is concluded that the entire instability of the pressure-arch is caused by local damage and the failure models of local damage has three forms, namely tension-failure, shear-failure and compression-failure through the comprehensive analysis. The results show that with the increase of the dip angle of the coal seam, the failure modes of the pressure-arch change from compression-failure at the arch-waist and shear-failure at the skewbacks to shear-failure at the vault and tension-failure at the front of skewback. It is of meaningful to direct the engineering practice.