Abstract: For the rock slope with many complicated discontinuities, the selection and analysis of the discontinuities are a very important work. The traditional analysis methods are insufficient and inadequate. The analysis results have a lot of subjective factors, and are inconvenient to be applied in practice. The selection and analysis of intersection lines of discontinuity are treated as the starting point. With the aid of stereographic projection, the possible sliding zone of sliding wedge can be first determined. The possible sliding line of intersection can be selected. So the range of calculation can be reduced. The symmetric axis center is used as the initial rallying point. The dominant orientations of discontinuities can be selected and analyzed through the probabilistic analysis of the stereographic projection based on the K-means clustering algorithm. A case study on a rock slope in Chongqing is used. The study shows that the results are reliable and reasonable, and the dominant orientations and classification are more precise.