Abstract: The block rock slope is made up of blocks and structural surfaces, and the stability of the rock mass is controlled by the existence and the strength of structural surface. Researches on the stability of block rock slope are carried out by using the lower bound theorem of plastic limit analysis, block discretization technique and mathematical programming method. Firstly, the slope is discretized into block assemblages that consist of rigid blocks and structural surface, considering the integral interaction of each other. And then, regarding the safety factor of slope stability as the objective function, the nonlinear mathematical programming models are established based on the lower bound theorem, which satisfy the equilibrium equations, yield conditions and static boundary conditions. The solution strategies of models are put forward, and the calculation programs are compiled. Finally, four classic examples are analyzed by means of the proposed method, and the rigorous lower limit values of the strength safety coefficient of slope, and the corresponding statically admissible stress fields are obtained. The results are compared with those produced by other classical approaches, and the validity of the proposed method is indicated.