Recently, a general methodology of analyzing electromagnetic scattering from one-dimensional and two-dimensional random rough surfaces was developed. In this article, the concept is extended to present a sparse-matrix canonical-grid method for the scattering of dense media. A dense medium of Np randomly located cylindrical scatterers of a uniform radius is considered. The near and intermediate range interactions in the medium are represented by the strong interaction matrix. For the weak part of the interaction among the cylinders, a uniform grid of Ng grid points is used as the canonical grid. Finally, the strong interactions between two cylinders in the vicinity of each other are calculated directly while the weak interactions between two distant cylinders are calculated indirectly.