Abstract: Using the concepts and method of finite-part integrals, the hypersingular integral equations of a plane crack loaded by arbitrary loads is proved exactly. The behaviour of the unknown solution are analysed theoretically and its indexes are then obtained. Based on these results, the singular stresses near the smooth point of the crack front are exactly derived by use of the dominant analyses. Then the stress intensity factors are expressed in terms of the displacement discontinuities of the crack surface. Fi...