The tuning of the low frequency sound absorption of open-cell anisotropic porous materials is studied in the form of an optimisation problem. Using modelling based on micro-structural representations of the anisotropic elasticity, the dynamic viscous drag forces and cell porosity, a physically meaningful dependence between these quantities is ensured. The micro-geometry used here is Kelvin Cell based, which may be distorted in a controlled way, creating a degree of anisotropy in the dynamic viscous drag forces and the elastic properties. Here, the distortions are implemented through twisting the square faces of the cells, resulting in a controllable interaction between shear and compression in the elastic deformation. Low frequency sound absorption is maximised using a gradient-based optimisation approach. Importantly, the design parameters in this approach are purely geometrical: the twist angles, strut radii and the respective layer thicknesses. A multi-layer arrangement undergoing plane wave acoustic excitation is considered as an application example.