A computational method for analyzing the two-dimensional multiple scattering of elastic waves in unidirectional fiber-reinforced media, consisting of elastic cylindrical fibers arranged in an infinitely extended elastic matrix, is presented. The method is based on the eigenfunction expansion of the displacement potentials and the numerical collocation technique to obtain the expansion coefficients. In the present study, the formulation is extended to incorporate the presence of a coating layer between the fibers and the matrix. As an example, the transmission characteristics of longitudinal as well as transverse waves in a unidirectional composite with square array of fibers are analyzed, and the phase velocities in the composite are evaluated. The effect of the coating layer on the wave transmission and stop-band formation behavior is also demonstrated. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).