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This paper describes advanced finite-element simulations of a geologically active and periodically unstable 700 m high underwater escarpment located in the Gulf of Mexico that has been created by uplifting salt diapirs combined with sediment deposition. The site's geological history, soil permeability and clay shear strength characteristics govern current slope stability, and determine the timing of any future failure. The geological and geotechnical conditions are reported before presenting fully coupled, large-displacement numerical simulations employing critical state formulations of the slope's evolution over the last 600 000 years. The latter form the basis for strain-softening analyses of the pore pressure equalisation and progressive failure processes that control current slope stability. The analyses also address the ground movement patterns that precede instability, giving useful information for geohazard risk assessment and early warning monitoring system design. [ABSTRACT FROM AUTHOR]