SArch bridge is the main bridge type in the western canyon. The stability analysis of the rock slope at the foundation is an important part of the arch bridge design. The stability of the slope is controlled and affected by the structural plane of the rock mass. The stereographic projection method is a practical, convenient, fast and effective method for analyzing the stability of rock slopes. In this paper, in conjunction with an arch bridge project in the Chongqing Canyon area, the basic principles and use methods of stereographic projection are explained in detail, and the stability analysis and reinforcement plan of the rock slope of the arch bridge arch abutment in the canyon area are put forward. The project provides a useful reference.