For applications of porous materials where mean pressure drop is a concern, packaging the material into a corrugated structure is better compared to other geometries such as block or wedge shapes. The goal of this study is to integrate noise reduction functionality within that material, which requires an understanding of sound propagation through corrugated porous structures, including flow effects. The corrugated porous structure involves porous partitions separating inlet and outlet fluid channels. The porous materials considered are periodic octet-truss and body-centered cubic unit cells, and sound propagation across these porous partitions is modeled using the Johnson–Champoux–Allard model. The predicted transmission loss (TL) is benchmarked using designed additively manufactured corrugated structures measured using a flow duct. The laminar flow regime is maintained across the porous structure to reduce flow-noise effects. It is shown that the TL for a given corrugated structure increases with a decrease in porosity, and the impact of flow becomes significant as the porosity decreases. The influence of flow on TL also depends on the unit cell configuration. Furthermore, the model provides insights into pressure and acoustic particle velocity distributions within the corrugated structure and reveals regions of the porous material that effectively participate in noise reduction.