For a quantitative analysis and better understanding of the stress-strain response and their effects on interface debonding and crack initiation and propagation of alternative hard and soft multi-layers under circumscription loading, to explore methodologies of optimum design of surface multi-layers, large strain elasto-plastic finite element method is used to evaluate the mechanical behaviors of TiN/Ti multi-layer films on rigid substrate under hard asperity indentation. The results show that with the same total thickness of the film, the alternate hard and soft multi-layers with larger ratio could endure larger circumscription loading, and the different total thickness of multi-layers could affect the circumscription loading greatly. So there must be a circumscription loading in this multi-layer film structures. Generally speaking, the circumscription loading has something to do with the material modulus, the radius of the press-head, the thickness ratio of soft and hard layers, and the total thickness of alternate hard and soft multi-layers. For a quantitative analysis of this problem, finite element method is utilized to analyze the phenomena of the plastic indentation. According to analysis of the film deformation, the maximum bending stress, and the surface bending stress, and those parameters that have influence on different alternative films are studied. The study of this paper is expected to provide some theoretical basis for the optimum design of multi-layer film structures.