Abstract: Approximate J-estimation methods including the weld mis matching effects for a circumferentially surface cracked pipe with an internal,constant depth and finite length surface flaw under pure bending are developed.These are referred to SC.ENG3 and SC.ENG4 in corresponding to SC.ENG1 and SC.ENG2 methods.It is assumed that the Ramberg-Osgood power-law and the plasticity deformation theory control the stress strain response of the base and the weld material.The closed form J-solutions in terms of elementary functions are derived from the classical beam theory combined with an equivalence criterion.Several numerical examples of pipe welded joints are presented to verify the feasibility of the proposed methods.