Propagation of elastic waves in a system of cylindrical channels embedded in a homogeneous isotropic elastic medium (a phononic crystal) is investigated. A multipole method is proposed for simulation of wave propagation in such structures. The dispersion characteristics of wave propagation in systems consisting of three, six, and seven cylindrical channels are calculated. The results are compared to the data corresponding to wave propagation along a single channel. The computational efficiency of the method and its applicability to simulation of the propagation of elastic waves in large phononic crystals are assessed.