Abstract: Using the limit equilibrium approach, the problem of passive earth pressure on rigid retaining wall is formulated in terms of variation calculus with Lagrange multipliers, and is transformed as the functional extreme-value problem of two variables. It is further transformed into the solution of extreme value of restrained functions incorporating the geometrical relations of the forces. Computation results show that there exist two kinds of failure modes - sliding along a plane surface (translation) and rotation along a log-spiral cylinder surface (rotation) when the soil behind retaining walls reaches critical passive state. In the translational failure mode, the passive earth pressure coincides with the theories of Coulomb (1776) and Rankine(1857); in rotational failure mode, the passive earth pressure agrees well with that of Chen(1975) and Sokolovskii(1956). Comparisons with measured data indicate that the ordered real number pair predicted by the two theoretical theories can be regarded as an interval estimation of passive pressure, which comprises the earth pressures on the rigid retaining wall with any wall movement.