Abstract: Based on the force equilibrium equations of the sliding mass, the problem of active earth pressure and passive earth pressure was transcribed as the functional extreme-value problem of two undetermined function arguments by means of Lagrange multiplier, and was further transformed into determining the minimax solution of restrained functions incorporating the geometrical relations of the problem. The function of fmincon in the optimization toolbox of MATLAB 6.1 could be used to find the minimax solution. The relative positions of the action point of earth pressure on the wall were calculated after having found the dimension of active earth pressure and passive earth pressure, using the moment equilibrium of the sliding mass. The failure wedge sliding along plane surface is the theoretical-derived conclusion, and the magnitude of active earth pressure attained is the same as that of Coulomb (1776), but the location of application point of earth pressure is not always at 1/3 height of the retaining wall.