The failure of the Kettleman Hills landfill focused attention on the uncertainties associated with the use of limit equilibrium analyses for evaluation of the stability of slopes in which failure occurs along displacement-softening interfaces. Sliding on such interfaces can occur in a progressive manner with the result that the available interface strengths are reduced below their peak values. The amount of strength reduction depends on the magnitude of shear displacement, which varies from one location to another. Because the limit equilibrium method does not provide any information regarding the magnitudes of shear displacements along the sliding interface, it can only provide realistic assessments of stability where progressive failure effects are small, or where the degree of strength reduction due to progressive failure can be estimated independently. The objective of this research study was to develop procedures to study the phenomenon of progressive failure in lined landfills, and to use the results of these studies as a basis to provide guidance for performing limit equilibrium analyses. Progressive failure along liner interfaces was analyzed using the finite element method. Adaptation and application of the finite element method for this type of analysis was a principal focus of this study. Two new plasticity models for interface behavior, a displacement-softening model and a work-softening model, were developed to simulate strength reduction along liner interfaces. The work-softening model performs better than the displacement-softening model when applied to laboratory tests performed under conditions of changing normal stress. However, the differences in performance of the two models were not significant when applied to landfills. The displacement-softening model is computationally more efficient, and it was used in most of the analyses. Progressive failure effects were severe for all the cases that were analyzed in this study. Analyses of the Kettleman Hills failure showed that the average available shearing resistance at failure was only about 10 percent higher than the residual shearing resistance. Analyses of hypothetical Municipal Solid Waste landfills indicated that the average available shearing resistance would be about 6 percent to 14 percent greater than the residual shearing resistance. This means that a limit equilibrium factor of safety of 1.4 based on residual strengths would correspond to a factor of safety of 1.5 if progressive failure was taken into account. / Ph. D.