The main purpose of this article is to present, within a unified framework, a technique based on numerical homogenization, to model the acoustical properties of real fibrous media from their geometrical characteristics and to compare numerical results with experimental data. The authors introduce a reconstruction procedure for a random fibrous medium and use it as a basis for the computation of its geometrical, transport, and sound absorbing properties. The previously ad hoc "fiber anisotropies" and "volume weighted average radii," used to describe the experimental data on microstructure, are here measured using scanning electron microscopy. The authors show that these parameters, in conjunction with the bulk porosity, contribute to a precise description of the acoustical characteristics of fibrous absorbents. They also lead to an accurate prediction of transport parameters which can be used to predict acoustical properties. The computed values of the permeability and frequency-dependent sound absorption coefficient are successfully compared with permeability and impedance-tube measurements. The authors' results indicate the important effect of fiber orientation on flow properties associated with the different physical properties of fibrous materials. A direct link is provided between three-dimensional microstructure and the sound absorbing properties of non-woven fibrous materials, without the need for any empirical formulae or fitting parameters.