An iterative boundary element method, which was originally developed for both two- and three-dimensional cavitating hydrofoils moving steadily under a free surface, is modified and extended to predict the wave pattern and wave resistance of surface piercing bodies, such as ship hulls and vertical struts. The iterative nonlinear method, which is based on the Green theorem, allows the separation of the surface piercing body problem and the free-surface problem. The free-surface problem is also separated into two parts; namely, left and right (with respect to x axis) free-surface problems. Those all (three) problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The wetted surface of the body (ship hull or strut, including cavity surface if exists) and the left and right parts with respect to x axis of free surface are modelled with constant strength dipole and constant strength source panels. In order to prevent upstream waves, the source strengths from some distance in front of the body to the end of the truncated upstream boundary are enforced to be zero. No radiation condition is enforced for downstream and transverse boundaries. A transverse wave. cut technique is used for the calculation of wave resistance. The method is first applied to a point source and a three-dimensional submerged cavitating hydrofoil to validate the method and a Wigley hull and a vertical strut to compare the results with those of experiments. Copyright (C) 2007 John Wiley & Sons, Ltd.