This paper presents a method for the mechanical characterization of anisotropic foams. The objective of this study is to determine the static elastic parameters of an acoustic foam. The approach is based on measurements of the stiffness of samples in static compression and shear tests. The elastic constants are recovered through an inverse estimation method, by performing a fit of a numerical model (finite element method) with the measured stiffness of the porous material. The material is modeled as an orthotropic equivalent solid, whose principal directions are aligned with the coordinate system in which the experiments are conducted. A numerically generated target material is used here as a benchmark in order to show the efficiency of the approach. The method is applied to polyurethane (PU) foam, which is found to have orthotropic properties with highest stiffness in the direction parallel to the rise direction of the material.