Abstract: Based upon a comprehensive study of the various methods of slices for slope stability analysis, the general equilibrium equations have been put forward. Extensions have been made to the Morgenstern-Price method which is known to be a rigorous method for solving the equilibrium equations. They include:1. The argument about the restrictions on the boundary values of the unknown variables when assumptions are made for them.2. A refinement of the numerical process to solve the convergence problems which have occasionally affected other methods in common use.3. The development of a numerical procedure based on the calculus of variations which has made it possible to find the upper and lower bound of the safety factors subjected to the restrictions of physical admissibility. The rigorous solution for the factor of safety has accordingly been obtained.