A displacement superposition method based on the principle of compatibility of deformation is approached for solving multi contact problems.The formulas derived in this paper has been programmed to solve the load distribution between the teeth of a turbine disk lugs in association with FEM program,and then the maximum stress at each fillet of tooth is calculated.A study on fracture mechanics of the disk lug with different cracks in the tooth fillet is also presented.The results are in satisfactory agreement with data of the photoelastical experiments.