Boundary integral equation methods for computing two- and three-dimensional nonlinear free surface flows are presented. In two dimensions, integral formulations can be derived by using complex variables or Green's functions. Both formulations are shown to yield the same level of accuracy. The formulation based on Green's functions is extended to three dimensions by following Forbes [J. Comput. Phys. 82 (1989) 330-347] and accurate numerical results are presented for moving distributions of pressure and moving submerged disturbances. (C) 2002 Editions scientifiques et medicales Elsevier, SAS. All rights reserved.