This paper presents applications of an inverse method for the design and characterisation of anisotropic elastic material properties of acoustic porous materials. Full field 3D displacements under static surface loads are used as targets in the inverse estimation to fit a material model of an equivalent solid to the measurement data. Test cases of artificial open-cell foams are used, and the accuracy of the results are verified. The method is shown to be able to successfully characterise both isotropic and anisotropic elastic material properties. The paper demonstrates a way to reduce costs by characterising material properties based on the design model without a need for manufacturing and additional experimental tests.