A method is developed for the numerical evaluation of the integral solution to the wave equation for a point source in shallow water overlying a “hard” liquid type bottom; i.e.,c2>c1. This method is especially useful for intermediate horizontal ranges where satisfactory approximations to the sound field have not been found. In general the integral cannot be evaluated directly because there are singularities in the integrand. Instead it has been transformed into the complex plane in such a way that the resulting integrals and residues can be evaluated on a high speed digital computer. A limited number of calculations were made to illustrate the use of the numerical method.