An integral equation is formulated for the scattering problem by the planar periodic array of scatterers. In this case, the fundamental solution is in a form of double series and the series may converge very slowly in a certain configuration of periodic scatterers. In this paper, a practical numerical integration based on Ewald method is investigated for the fundamental solution with the double infinite series. In more detail, the fundamental solution is converted into the integral form with rapidly convergent integrand and the Gauss’ numerical integration is performed here to evaluate the integral. The convergence and the efficiency of the method are demonstrated numerically for the integral equation by the planar array of scatterers. The reflection and transmission coefficients are calculated as an application of the present numerical evaluation for the fundamental solution. ©2000 American Institute of Physics.