A new method is described for evaluation of electric field around rectangular arrays of large charged spheres of alternating sign. It is shown that the arrays can be simulated by three pairs of point charges per unit cell. The relation between spacing of charges, their intensity, and radius of the spheres yields the required field. The method provides superior accuracies for different unit cell proportions, including a cube and rectangular parallelepipeds, with the point charges appropriately arranged so as to satisfy boundary conditions.