Time-dependent behavior of natural and excavated slopes in sedimentary rocks is a subject that is poorly understood at present but that is now an important consideration in the design, operation, and reclamation of energy-extraction facilities, in part because of the environmental considerations mandated by the Surface Mining Control and Reclamation Act of 1977 (Public Law 95-87). A slide in an abandoned, unreclaimed strip mine northwest of Sheridan, Wyoming, has been analyzed as an example of a long-term slope failure in the region. This slide occurred in early 1975, some 20 years after cessation of mining. This investigation used Spencer's limiting equilibrium method and an elastic-plastic finite element method incorporating the Drucker-Prager yield criterion. This slide was found to fit the model for time-dependent failure proposed by Nelson and Thompson (1977) in which the time to failure is related to Skempton's residual factor. The Nelson-Thompson hypothesis is extended for use with the three-dimensional Drucker-Prager yield criterion. The residual factor (R) may be computed from the factors of safety with respect to peak (F(p)) and residual (Fᵣ) material properties, using either the Mohr-Coulomb or Drucker-Prager criterion, by the relationship R = [(F(p) - 1)/(F(p)-Fᵣ)] At the present time, the Spencer limiting equilibrium analysis is a more usable tool for ordinary slope design than the elastic-plastic finite element analysis because of the speed, simplicity, and ease of including the effects of ground water in the Spencer analysis.