Fracture analysis is performed on a cylindrical composite consisting of an outer elastic layer, an inner rigid cylinder and an intermediate sliding interface. Interaction between the sliding interface and a parallel crack under in-plane shear is explored. An interesting phenomenon of oscillatory normal stress occurs on the local interfacial region near to the crack. It leads to local sliding-prevention and promotion effects, which constitute the mechanisms for the variations of stress intensity factors versus interfacial parameters. In addition, another interesting conclusion is that a crack near and parallel to a sliding interface never has the conventional anti-symmetry, even under pure in-plane shear loading.