We present a new method to accurately calculate the electrostatic energy and forces on charges being distributed in a two-dimensional periodic array of finite thickness. We transform the Coulomb sum via a convergence factor into a series of fast decaying functions which can be easily evaluated. Rigorous error bounds for the energies and the forces are derived and numerically verified. Already for small systems our method is much faster than the traditional 2D-Ewald methods, but for large systems it is clearly superior because its time demand scales like C(N-5/3) with the number N of charges considered. Moreover it shows a rapid convergence, is very precise and easy to handle. (C) 2002 Elsevier Science B.V. All rights reserved.