Bonded joints are very common in many pipeline systems, in which the bond behavior of the joint interface is of crucial importance. This paper presents two analytical solutions for the debonding process of a pipe joint under torsion, assuming that the bond interface follows either an exponential softening bond-slip law or a simplified bilinear model. The solutions are general, applicable to composites and metallic and indeed other pipes. Based on the analytical solutions, the influences of the bond length and stiffness on the torque-displacement curve and ultimate load are investigated. The solutions can be used to explain the stress transfer mechanism, the interface crack propagation, and the ductility of the joint.