Multiscale homogenization represents a powerful tool to treat certain fluid-structure interaction problems involving porous, elastic, fibrous media. This is shown here for the case of the interaction between a Newtonian fluid and a poroelastic, microstructured material. Microscopic problems are set up to determine effective tensorial properties (elasticity, permeability, porosity, bulk compliance of the solid skeleton) of the homogenized medium, both in the interior and at its boundary with the fluid domain, and an extensive description is provided of such properties for varying porosity. The macroscopic equations which are derived by homogenization theory employ such effective properties thus permitting the computation of velocities and displacements within the poroelastic mixture for two representative configurations of standing and travelling waves. (C) 2018 The Authors. Published by Elsevier Ltd.