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International audience; The ability of air-saturated fibrous media to mitigate sound wavesiscontrolled by their transport properties that are themselves controlled by the geometrical characteristics of their microstructure such as the open porosity,fiber radius, and fiber orientation. Here, micro-macro relationships are proposed to link these microstructural features to the macroscopic transport properties of random fiber structures. These transport properties are the tortuosity, the viscous and thermal static permeabilities, and the viscous and thermal characteristic lengths. First, representative elementary volumes (REVs)ofrandom fiber structures are generated for different triplets of porosity,fiber radius and fiber orientation. The fibers are allowed to overlap and are motionless (rigid-frame assumption). The fiber orientation is derivedf rom as econd order orientation tensor.S econd, the transport equations are numerically solved on the REVs which are seen as periodic unit cells. These solutions yield the transport properties governing the sound propagation and dissipation in the respective fibrous media. From these solutions, micro-macro relationships are derivedt oe stimate the transport properties when the geometry of the fiber structure is known. Finally,these relationships are used to study the influence of the microstructural features on the acoustic properties of random fiber structures.