The variational limit equilibrium method is adopted to calculate the active earth pressure with and without tension cracks appearing. According to static equilibrium equations of sliding soil, a functional extreme-value isoperimetric model of cohesive soil is deduced in the general case of an inclined wall, sloping backfill, and uniform surcharge on the backfill surface. The active earth pressure is caculated by a functional extreme-value problem of two unknown functions through introducing two undefined Lagrange multipliers. According to the corresponding Euler equations and the boundary conditions, functions of the sliding surface and the normal stress distribution along the sliding surface, which contain two undefined Lagrange multipliers, are deduced.