The effects of relative alignment of two different types of anisotropic open cell porous materials are investigated in terms of the acoustic response of a multi-layered configuration. Numerical experiments, where gradient based optimization techniques were used, are conducted to find possible extremal values. It is shown that, depending on the degree of anisotropy of the porous material properties, their angular orientations have a significant and frequency dependent influence on the measured response. The results highlight the importance of further advancing the knowledge of anisotropic porous material behavior.