The slope stability is an important factor affecting the safety of earth-rockfill dam. Sweden arc and simplified Bishop methods are usually used to calculate the slope stability of earth-rockfill dam, although the calculation results are not the lower or upper solutions. On the basis of Sloan’s work, a finite element method is used to discretize the mechanism. The effective statically admissible stress fields can satisfy the conditions of equilibrium, stress boundary, yielding and stress discontinuity, the earthquake action and the seepage action. They are taken into account. Using the idea of nonlinear programming, a lower bound limit analysis model of mathematical programming for the slope stability of earth-rockfill dam is established. The model can evaluate the slope stability factor of earth-rockfill dam and get the stress field of lower bound. The nonlinear strength indexes and iterative algorithm are also used for the stability calculation and the corresponding program is compiled. Finally, the stability of some typical soil slopes and specific earth-rockfill dams is calculated. The results are compared among the results of many other methods. They indicate the correctness of the method and the program.