One of the main issues in designing earth structures is to ensure their slope stability. To analyze the stability of soil mass affected by seepage forces a new method has been proposed where all equilibrium conditions and boundary conditions at the ends of the surface profile are satisfied by strain and orientation of areas of shear. To find the most hazardous hypothetical failure surface a variational method was used, which involves solving Euler-Lagrange differential equation as a necessary condition for the existence of functional extremum. Since the problem can be solved in the framework of the scheme of limit equilibrium of soil masses with the use of the Mohr-Coulomb strength criterion, one of the parameters of soil strength acts as a functional for the given values of another parameter. Sufficiency of the existing functional extremum is verified numerically.