Multiple scattering of elastic waves by randomly distributed cylinders of arbitrary cross section has been considered. Because the pair‐correlation function, as well as the quasicrystalline approximation, has been incorporated in the presented formalism, the effective phase velocity, as well as the coherent attenuation in dense systems, has been investigated. A more efficient scattering formalism (SF) has been employed rather than the exciting field formalism (EF) used earlier by the authors. Closed form expressions for the phase velocity and the attenuation are given in the Rayleigh limit, and numerical results are presented for a wide range of frequencies and concentrations.