AbstractIn this paper, the reciprocal work theorem for viscous fluid flow is established for Newtonian fluids and, based on this theorem, a set of boundary‐domain integral equations is derived from the continuity and momentum equations for two‐dimensional viscous flows. The complex‐variable technique is used to compute velocity gradients in the use of the continuity equation. The primary variables involved in these integral equations are velocity, traction and pressure. Although the numerical implementation is only focused on steady incompressible flows, these equations are applicable to solving steady, unsteady, compressible and incompressible problems. In this method, the pressure can be expressed in terms of velocity and traction such that the final system of equations entering the iteration procedure only involves velocity and traction as unknowns. Two commonly cited numerical examples are presented to validate the derived equations. Copyright 2004 John Wiley & Sons, Ltd.