This work presents a numerical model to estimate the exact permittivity for well calibrated periodically structured materials. The long wave approximation (LWA) has been employed to evaluate the field distribution in such systems when subjected to a prescribed potential on their boundary. The effective response leading to permittivity estimation has been conducted considering the macroscopic system to be a periodic array of "unit cells" representative of the minimum volume preserving macroscopic homogeneity. Our numerical estimations are carried out using a Monte-Carlo random walk iterative method. Instead of imposing the "non-reflecting boundary potential," we connect the potential onto the boundaries of the unit cell by the periodic Born-Von Karman condition. Values of the effective permittivity for certain aggregate systems of interest including percolating simple cubic structures are presented. (C) 2003 Published by Elsevier B.V.