Abstract: Under the impact of storm surge, earthquake and other uncertain factors, large scale sediment failure may be triggered along the submarine slope. In this paper, we try to brief the progress of submarine slope stability research both abroad and at home, with emphasis on methodology. Discussed were the GEO-SLOPE landslide analysis software, the total stress and limit equilibrium method and probability method for submarine slope stability calculation. The sliding model and slope finite element model were introduced for determining the model base material in a selected area, such as underwater terrain parameters, the stratigraphic parameters, soil strength parameters. Simulation was suggested for down slope stability reliability calculation under extreme conditions, such as storm and earthquake. Numerical analysis was introduced for study of slope instability probability.