Fibrous materials can efficiently dissipate acoustic energy, and their intrinsic properties are determined by fiber geometries (microscale). In this study, the effect of cross-sections of fibers on the transport and acoustic properties of fibrous materials was investigated. First, fibers of various cross-sections were modeled by adjusting their open porosity. The representative elementary volumes of fiber structures were generated to describe the periodic unit-cell structures. Next, the transport properties (such as static airflow resistivity, high-frequency limit of the dynamic tortuosity, viscous characteristic length, thermal characteristic length, and static thermal permeability) of fibrous materials were calculated by solving numerical problems using the finite element method. These properties of fibrous materials with complex cross-sections were compared with those with circular cross-sections. Finally, the sound absorption coefficients were predicted using the Johnson-Champoux-Allard-Lafarge (JCAL) model and rigid frame approximation, and the differences in sound-absorbing behavior were analyzed. This study can provide insights into the design of lightweight fibrous materials while maintaining optimal sound absorption performance.