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On the basis of the limit equilibrium method and the physical significance of Coulomb’s yield criteria, extremum conditions of yield functions is established, which will be the fundamental equations for the limit analysis of soil mass. Once the stress equation along a sliding surface is available, the normal stress on the sliding surface can be obtained, a new limit analysis method, generalized limit equilibrium method (GLEM), can be established. With the generalized limit equilibrium method, an analysis method to solve the problem of slope stability can be obtained without introducing any other assumptions or simplified conditions but the sliding surface. With this algorithm, any discretionally possible sliding surface can be trial calculated and the least value of the calculated results of different sliding surfaces is taken as the safety factor. As long as a selected sliding surface is close to the true sliding surface, the derived safety factor will be approximate to the genuine solution to a problem of slope stability.