<p>Porous media are commonly described as effective isotropic fluid materials, such that their acoustic properties can be adequately determined from their bulk modulus and dynamic density. Most porous materials, however, possess a marked anisotropy, which influences their acoustical behavior and the parameters necessary to deduce it. Specifically, the influence of anisotropy translates into a full symmetric density tensor, drastically increasing the number of effective fluid parameters required to describe the medium. This paper presents a method for retrieving the bulk modulus and density tensor coefficients of a rigidly-backed layer of anisotropic porous material from reflection coefficients measured in free field with an array of microphones. The procedure consists in estimating the reflection coefficient via sound field reconstruction at the material’s surface. The reflection properties are estimated for various angles of incidence, and an inverse problem is formulated to infer the effective fluid parameters. The validity of the method is confirmed numerically on a synthetic porous layer and experimentally on a manufactured glass wool layer. The proposed method enables to characterize anisotropy in porous media non-invasively (solely based on observing the sound field above the material), showing promising potential for the effective characterization of complex media.</p>