A new computational approach for calculation of the effective transverse mechanical properties of unidirectional fiber-reinforced composites with linear viscoelastic matrix and elastic fibers is presented. The approach requires the knowledge of stresses outside a cluster representing the structure of composite in question. The effective properties are found from the assumption that the viscoelastic stresses at the distances far away from the cluster are the same as those from a single equivalent inhomogeneity. The approach directly takes into account the interactions between the inhomogeneities. The comparison of the results with several benchmark solutions reveals the advantages of the developed approach.