This paper presents a theoretical analysis of sound transmission through a sandwich structure in the presence of external mean flow. The structure is comprised of two panels connected by two-layered pyramidal cores and filled with fibrous material. The fibrous absorptive material in the core is characterized by an equivalent fluid model. The interaction between the structure and the surrounding fluid is taken into account by imposing a velocity continuity condition at the interfaces. The inclined beams in the core exert forces and moments on the panels. The space-harmonic approach and virtual work principle are applied to derive the governing equations. A validation is carried out by comparison with finite element simulations and existing experimental measurement. Numerical calculations are used subsequently to explore the influence of the material, mean flow and structure geometry. The results demonstrate that the absorptive material influences the sound transmission loss (STL) at low frequencies and that the effectiveness is affected by the geometry of the structure.