The shape,position and stress distribution on the sliding surface can be rationallydetermined by a variational method.And the method satisfies the equilibrium,yield condition and thetransversal conditions for the unknown position to determine the critieal height of a slope when theslope angles and the material parameter C and are known.This paper corrects some ertors existingin the current literature and presents two curves to facilitate deterimination of the critical height andthe cracking position appearing on the top surface of the slope.These curves are particallarly suitedto backanalysis of landslide when the cracking position,the originally slope angle and the failuredslope height are known or can be estimated.Finally,calculated examples are cornpared with currentliterature.