Taking right dam abutment slope of Miaojiaba hydropower station as an example, Studying the failure modes of the abutment slopes in natural status and their geological evolving process,and with the results from the above study predicting the failure modes of the abutment engineering slopes. All those two works being done by using stereographic projection method and based on the characterization of prominent discontinuities and random discontinuities. Such doing concerns not only interrelations, formation causes and characteristics of discontinuities, but also geological evolving process of failure modes,which presents synthetical thinking on the study of slope failure modes.