The extreme conditions of yield condition and yield function are discussed; and a velocity equation is established under the condition that no flow rule has been required. The equilibrium equation

extreme conditions of yield condition and yield function

and velocity equation are the fundamental equations for limit analysis of soil mass

which constitute a complete limit equilibrium problem of the boundary conditions for loading and velocity

including the coexistence of boundary conditions for loading and velocity. The upper and lower bound theorem of slope stabilization is rigorously proved; and a generalized method of limit equilibrium has been established to solve the problem of limit equilibrium. The calculated result of homogeneous soil indicates that the generalized method of limit equilibrium for a circular slip surface is basically identical with the upper bound solution for a logarithmic spiral surface.