The kernels of integrands are usually differentiated to obtain the general boundary integral equation (BIE) for stresses and its corresponding traction equation. An alternative BIE for stresses can be obtained when the tangential differential operator is introduced in problems using Kelvin type fundamental solutions. The order of the singularity is reduced with this strategy and the Cauchy principal value sense or the first order regularization can be used in the resultant BIE. The dual boundary element formulation with the BIE for tractions using the tangential differential operator is analyzed in the present study. Shape functions with same expressions for conformal or non-conformal interpolations are adopted and conformal interpolations were applied on the crack surface without losing the accuracy of the dual formulation. The results obtained are compared with solutions available from the literature to evaluate the formulation. Copyright © 2006 Tech Science Press.22123130Aliabadi, M.H., Boundary element formulations in fracture mechanics (1997) Appl. Mech. Rev., 50, pp. 83-96Almeida, L.P.C.P.F., Palermo Jr., L., On the implementation of the two dimensional dual boundary element method for crack problems (2004) 5th Int. Conference on Boundary Elements Techniques, , Lisboa, PortugalBlandford, G.E., Ingraffea, T.A., Liggett, J.A., Two-dimensional stress intensity factor computations using the boundary element method (1976) International Journal of Numerical Methods in Engineering, 17, pp. 387-404Bonnet, M., (1999) Boundary Integral Equation Methods for Solids and Fluids, , JohnWiley & Sons LtdChen, W.H., Chen, T.C., An efficient dual boundary element technique for a two-dimensional fracture problem with multiple cracks (1995) International Journal of Numerical Methods in Engineering, 38, pp. 1739-1756Civelek, M.B., Erdogan, F., CRACK PROBLEMS FOR A RECTANGULAR PLATE AND AN INFINITE STRIP. (1982) International Journal of Fracture, 19 (2), pp. 139-159Crouch, S.L., Solution of plane elasticity problems by the displacement discontinuity method (1976) International Journal of Numerical Methods in Engineering, 10, pp. 301-342. , 1976Guiggiani, M., Hypersingular formulation for boundary stresses evaluation (1994) Eng. Anal. Bound. Elem., 14, pp. 169-179Guimarães, S., Telles, J.C.F., General application of numerical Green's functions for SIF computations with boundary elements (2000) CMES - Computer Modeling in Engineering & Sciences, 1, pp. 131-139Kupradze, V.D., (1979) Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity, , North HolandMi, Y., Aliabadi, M.H., Dual boundary element method for three-dimensional fracture mechanics analysis (1992) Engineering Analysis with Boundary Elements, 10 (2), pp. 161-171. , DOI 10.1016/0955-7997(92)90047-BMurakami, Y., (1987) Stress Intensity Factors Handbook, , Pergamon Press, OxfordPortela, A., Aliabadi, M.H., Rooke, D.P., The dual boundary element method: Effective implementation for crack problems (1992) International Journal of Numerical Methods in Engineering, 33, pp. 1269-1287. , 1992Sladek, V., Sladek, J., THREE-DIMENSIONAL CURVED CRACK IN AN ELASTIC BODY. (1983) International Journal of Solids and Structures, 19 (5), pp. 425-436Snyder, M.D., Cruse, T.A., Boundary integral equation analysis of cracked anisotropic plates (1975) International Journal of Fracture, 11, pp. 315-342Wen, P.H., (1996) Dynamic fracture mechanics: Displacement discontinuity method, , Computational Mechanics Publications