The two-dimensional steady potential free surface flow due to a pressure distribution moving at a constant velocity at the surface of a fluid of infinite depth is considered. The effects of gravity and surface tension are included in the dynamic boundary condition. The fully nonlinear problem is solved numerically by a boundary integral equation method and the results are compared with those of the linear theory of Rayleigh (1883). It is found that for some values of the capillary number, the nonlinear solutions do not approach the linear solution of Rayleigh as the magnitude of the pressure distribution approaches zero. Appropriate linear and nonlinear solutions are constructed.