Abstract: In this paper, based on the assumptions that the slip and the normal stress distribution over the slip surface are represented by Lagrangian interpolation functions, the horizontal and vertical forces and moment equilibrium equations for a sliding body are derived incorporating the effect of a passive earth force. The most dangerous failure surface and minimum passive earth pressure can be readily determined by the principle of optimality with force and moment equilibrium conditions satisfied. The present method deserves application to general engineer since it is free of complexity of conventional limit equilibrium methods of slices, as well as has advantages over other approximate methods of poor accuracy to a large extent.