Extensions are suggested to the generalized method of slices that is commonly used in slope stability analysis. It is shown that restrictions exist on the assumptions used to make the problem statically determinate. In addition, a numerical procedure has been developed to find the bounds to the factor of safety, subject to additional requirements of physical admissibility. As a result of these developments it has been possible to produce a revised computer program that appears to overcome the problems of convergence experienced by other programs in current use. Results obtained with this new analysis confirm the reliability of several methods of analysis used in practice.