Abstract: The numerical lower bound limit analysis of structural and plane strain elements could be applied to analyze a wide range of stability problems involving soil-structure interaction.The lower bound analysis was formulated as second-order cone programming problem,solved by primal-dual interior point method,whose objective function was the maximization of the applied external load subjected to the constraints of a static admissibility.The failure of structural elements was allowed to occur under combined bending,shear and axial force,and the failure envelopes of free-head piles with combined horizontal load and moment were generated.It was shown clearly that the capacity of the laterally loaded piles H/(cL) was a function of the relative strength parameter Mp/(cL2),where H was the horizontal load applied at the top of the wall,L was the pile length,Mp was the plastic moment of the pile,and c was the undrained shear strength of clay.The results obtained for rigid piles agreed with approximate solutions of Davis(1961).The first application of this combined formulation to analyze a laterally loaded pile embedded in a homogeneous clay layer was presented.