Abstract: The features of geotechnical slope structures are studied in the fields of mining industry, hydropower and highway. The corresponding analysis model and characterization indices for the new geotechnical slope structures are recommended based on the rigid sliding and deformation difference composite failure mechanism. By means of the robustness method of test design based on the arithmetical deviation theory, the principles of hypercube multidimensional space sampling are established. They are also used to reflect the highly nonlinear operator interaction among the factors which cause failures. The fuzzy grey correlation degree and the interval algorithm are deduced by embedding the fuzzy grey correlation rules into the interval model so as to solve the uncertainty and unknown problems existing in the factors. The input parameters in the calculation model are provided according to the sampling criterion. Meanwhile, the influencing parameters are displayed by the degree algorithm on the characterization of the sensitivity and importance degree index. They form a definite treatment method to demonstrate the failure mechanism of slope structures. Finally, the engineering application examples show the feasibility and effectiveness of the proposed method.