Underground pressure is abnormal during mining of shallow coal seams under gullies. We studied gully slope movements, subject to underground mining, with physical simulation and theoretical analysis. The rules disclose that the slope rock slides horizontally in response to mining in the direction of gullies and rotates reversely with the appearance of a polygon block in mining away from gullies. We focused our attention on the case of mining away from a gully. We built a mechanical model in terms of a polygon block hinged structure and investigated the variation of horizontal thrust and shear force at the hinged point in relation to the rotation angle under different fragmentations. The Sliding-Rotation instability conditions of the polygon block hinged structure are presented based on the analyses of sliding instability and rotation instability. These results can serve as a theoretical guide for roof control during mining away from gullies in a coalfield defined by gullies. Underground pressure is abnormal during mining of shallow coal seams under gullies. We studied gully slope movements, subject to underground mining, with physical simulation and theoretical analysis. The rules disclose that the slope rock slides horizontally in response to mining in the direction of gullies and rotates focusedly with the appearance of a polygon block in mining away from a gully. We focused our attention on the case of mining away from a gully. We built a mechanical model in terms of a polygon block hinged structure and investigated the variation of horizontal thrust and shear force at the hinged point in relation to the rotation angle under different fragmentsations. The Sliding-Rotation instability conditions of the polygon block hinged structures are presented based on the analyzes of sliding instability and rotation instability. These results can serve as a theoretical guide for roof control during mining away from gullies in a coalfield defined by gullies.