A technique for the numerical solution of two‐dimensional potential flow with a free surface and gravity is presented. Its validity is demonstrated by application to wave generation by a pressure on a segment of the free surface of a ponded fluid. Wave profiles are obtained for the leading waves of progressive approximately periodic wave formations that show the effect of retaining the nonlinear terms in the free surface boundary conditions. The programing is relatively simple and the technique applicable to other wave forming situations. However, long computation times are required.