Abstract: Based on the lower bound theorem of classical plasticity,the 3D limit analysis of rigid-perfect plastic structures was performed as a discrete nonlinear mathematical(second-order cone) programming problem by means of finite element technique.A statically admissible stress field was constructed derived from the solution of the lower bound nonlinear programming problem,which was obtained by primal-dual interior point method.The theoretical calculation framework was also presented.Both the linearization and the approximation process for 3D yield function could be removed by adopting nonlinear programming.Based on the duality with the lower bound and the upper bound,the solutions of the primal and the dual problem could be solved at the same time.The characteristics of rigid and flexible foundations were also discussed.It was shown by comparison with analytical solutions that the numerical analysis strategy was vastly superior in terms of the correctness and effectiveness of the procedure.A simple and effective computing method for the ultimate bearing capacity of foundations was provided by the 3D limit analysis.