On the basis of the upper boundary limit analysis theorem and nonlinear M-C failure criterion, three classical soil mechanics problems including the ultimate bearing capacity of a rough strip foundation, the critical height of a slope and the active soil pressure were studied by means of generalized tangential technique and the kinematic approach of limit analysis theory. The rationality and feasibility of the generalized tangential method and the inceptive tangential method were analyzed. From the numerical results, it can be seen that the nonlinear failure parameter exerts a significant effect on the safety of the geotechnical structure, and leading  in a proper nonlinear failure character of geo-materials more agrees with the engineering practice. The case study and comparative analysis show that a better solution could be achieved by means of the inceptive tangential method under specific conditions, but the larger the nonlinear coefficient is, the bigger the deviation caused by the inceptive tangential method is. The generalized tangential method possesses the rationality and feasibility obviously.