Based on the condition of plane strain and the static equilibrium equations for sliding mass considering strength reduction

the functional extreme-value isoperimetric model of homogeneous soil slope stability in the general case is derived. Based on that the Euler’s equations which must be satisfied when extreme value are obtained by functional analysis

the critical slip surface and the normal stress along the sliding surface are obtained by coordinates transform. Combined with the pre-defined boundary conditions and transversal conditions

the stability analysis for the soil slop is transformed to solving the minimum of a function with four unknown variables including two Lagrange multipliers

safety factor and x-coordinate of the slip end. The minimum of safety factor and the corresponding critical surface can be obtained by analytical computation. By taking the tensile cracks at the top of slope into consideration

the positions of different sliding surfaces and the corresponding safety factors are analyzed through a case study. In addtion

the proposed method is verified by ACADS slope test and the test results indicate that the predicted results consistent with the answer obtained by the judging procedure when the influence of the tensile crack is not considered

while the safety factor is slightly smaller than the answer obtained by the judging procedure when the tensile crack is considered.