A boundary element method has been developed that can be used to calculate two-dimensional potential flow phenomena with a free surface. The unsteady Bernoulli equation is applied at the actual position of the free surface. A solution for corners arising in the geometry of the boundary has been found. Comparison of results of the present model with results obtained with other numerical methods shows that reliable results can be obtained with the present model as long as the gap between two adjacent normals at a nodal point is less than about 40 degrees. At this limit the calculations break down. Within this limit, a forward directed jet is well developed in the case of breaking waves. The calculations can proceed if two points at the tip of the jet are considered as corner points. With these special points, the calculations can be continued up to the moment the jet falls down the forward face of the wave.