In order to numerically describe the whole failure process of bonded pipe joints under tension loads which is common in mechanical engineering, a cohesive interface modeling approach about debonding analysis of adhesively bonded interface of pipe joints is presented in this paper. A rigid-softening cohesive model was adopted to characterize the deformation of the interface. The whole failure process divided into different sections was discussed in detail and closed-form solutions of bond slip and shear stress were obtained. Finite element method (FEM) model for the bonded pipe joints under certain situations was established using commercial software ABAQUS, and the analytical and FEM results were compared. The stress transfer mechanism, the interface crack propagation and the ductility behavior of the joints under tension loads could be explained. These outcomes do help for the design and application of bonded pipe joints and can be extended to other orthotropic materials.