To improve understanding of evolution of submarine canyons, a three-dimensional slope-stability model is applied to Bourcart Canyon in the western Gulf of Lions in the Mediterranean Sea. The model builds on previous work by Chen and others, and it uses the upper bound theorem of plasticity to calculate the factor of safety of a kinematically admissible failing mass. Examples of three-dimensional failure surfaces documented in the literature were used to test the model formulation. Model application to Bourcart Canyon employed the results of a detailed stratigraphic analyses based on data acquired by swath bathymetry, sub-bottom profiling, high-resolution seismic reflection surveys, and piston coring. The sediment layers were also characterized using in-situ geotechnical measurements and laboratory tests. The effects of three loading scenarios were analyzed: (1) earthquake shaking, (2) hemipelagic sedimentation, and (3) axial incision. These three mechanisms influenced the predicted volumes and shapes of slope failures along the flanks of Bourcart Canyon, and comparison of these predictions with failure geometries inferred from seafloor morphology showed that mass failures could account for the observed morphology along the canyon walls as well as a mechanism of canyon widening