Abstract: The buckling and buckling failures are the two main problems in the process of stability analyses for bedding slope rock mass. In accordance with the occurrence characteristics and bifurcation properties of bedding slope rock mass and considering the situation that the research methods only use linear theory and the existing research results only stay at the level of structural buckling, this paper examines the buckling behavior and buckling failure behavior of bedding slope rock mass by using initial post-buckling theory and catastrophe theory, which gives the sliding conditions to an upper sliding section of bedding slope rock mass, derives its bifurcation equation and buckling failure equation, and points out the application conditions for the bifurcation equation and the application scope for the buckling failure equation. The lower limit of buckling failure in a state of post-buckling is determined, the criteria for buckling failure of bedding slope rock mass are built, and application with the example of the Bawang mountain slope located in the lower reaches of the Yalong River is presented. The results indicate that the occurrence situation for bedding slope rock mass determines its bifurcation set of potential function, the bifurcation load and bifurcation equation in a state of bifurcation can be derived from the bifurcation set for bedding slope rock mass. The solutions to the bifurcation equation describes the buckling state for bedding slope rock mass and also reflects the buckling criteria. The occurrence status for bedding slope rock mass also determines the scope of the material yield limit in a state of buckling failure, and either the upper or lower limit of buckling failure depends on the yield limit of rock mass material.