Abstract: The boundary integral equation (BIE) for evaluation of the warping shear stress is derived. The discontinuous boundary element is employed to discretize the boundary integral equation, where the physical quantities are approximated by discontinuous quadratic functions. The associated integrals are given in closed form. Numerical results are presented to demonstrate the efficiency and accuracy of this BIE in the analysis of thin-wall members. Due to the virtue of discontinuous elements and exact integration, the “boundary layer effect” associated with boundary element analysis is eliminated.