It is important to consider the pressure attenuations by fibrous material as well as rigid wall.To consider the pressure attenuation of fibrous material, this research develops a new acoustic topology optimization (ATO) framework with an empirical material formulation for fibrous material.To our best knowledge, despite the importance of considering pressure attenuation not only by internal solid structures but also by fibrous (porous) structures in acoustic design, a ATO approach with an empirical material formulation has not yet been developed.Thus, an empirical material formulation called the Delany-Bazley model is considered for the development of an ATO.By means of the SIMP (solid isotropic material with penalization) interpolation functions developed for multiple structural materials, ATO processes for fibrous structures as well as internal solid structures can be carried out.In addition, a heuristic filter method that allows fibrous material to emerge only at the boundaries or rims of an internal solid structure is presented..