As a typical model of steep-tilt or moderate-tilt bedding rock slopes, buckling failure differs greatly from tensile or shear failure. The mechanical characteristic of buckling failure is analyzed, and the geo-mechanics model of buckling failure is put forward. The process of buckling failure includes three phases: slope terrane creep deformation, the lower of slope terrane bend deformation, and terrane structure collapse. Using pressure bar failure theory, a formulation for calculating critical load of buckling failure is developed, which shows that critical load decreases with bend length increasing. The relationship between critical slope length and bend length is analyzed. It is indicated that critical slope length decreases with bend length increasing, and that critical slope length reaches minimal value while critical load is zero. The minimal slope length can be considered as a limit value while analyzing buckling failure of bedding slope, and its calculation equation is developed.