To understand the repair effect of trenchless centrifugal spraying method on defective pipeline and reveal the failure mechanism of the repaired interface and “pipeline-lining” system, a composite curved beam model was established. Analytical formulae of the cross section stress and the interface stress of the composite curved beam with different materials were derived by using the method of variable cross section, and the accuracy of the formulae was verified through the Three Edge Bearing Test (TEBT) of the repaired pipeline under concentrated load. The criterion for judging the coordinated deformation of the “pipe-lining” system was given—when the resistance of the interface was greater than the load, a composite structure was formed; otherwise, a unitized structure was formed. Through the analysis of the parameter study, a simplified interface shear stress formula was obtained based on the ratio β of lining thickness to host wall thickness,the ratio η of elastic modulus, and the diameter of the existing pipe D. The accuracy error between the proposed model and the mechanical model was less than 1%. Finally, the design method of lining repair for existing pipelines with different failure modes was given.