A numerical technique for solving scattering problems is presented. It is based on a boundary integral equation idea, so the unknowns are localized on the contour (in 2D case) or the surface (in 3D case) of the scattering object. Two major difficulties of traditional boundary integral methods (the appearance of spurious resonances and the necessity to perform numerical integration of singular functions) are overcome by studying the problem in an approximate discrete formulation from the very beginning. The space is filled by cubic blocks, and the shape of the scatterer is formed by a set of blocks removed from the space. Thus, the formulation of the problem is discrete and the continuous Green’s function is substituted by a discrete mesh Green’s function. An analogue of combined field boundary integral equation (CFIE) is developed for this formulation.