Abstract: There is no specific method which was widely used to analyze the deep anti-sliding stability of concrete gravity dam.The strength reduction method as a method to calculate the Factor of Safety(FOS) has many advantages on searching slide surface.75 examples of three typical geologic conditions were analyzed by the FLAC combined with strength reduction method and Morgenstern-Price method.The result shows that the errors of FOS obtained by FLAC strength reduction method and by M-P method are all below 5% and even smaller below 3.5% when associated flow rules are adopted in FLAC.A method to make sure the slide surface was obtained from the series of studies.The results in this paper indicate that the FLAC strength reduction method applied in the analysis of Xiangjiaba hydropower station is a new method which is reliable and feasible on the analysis on deep anti-sliding stability of concrete gravity dam.