Proper description of the resin flow through fibrous media is a very important input in the modeling of composite manufacturing processes. In this study, the complex phenomena associated with the flow of viscoelastic fluids through fibrous media are examined. In particular, the effects of fluid and fiber bed properties on the pressure drop observed during such flows were investigated, in conjunction with the specific conditions of typical composite manufacturing processes. To gain some insight into the problem, a theoretical and experimental investigation of Newtonian and non‐Newtonian flows through different geometric cylinder arrangements designed to simulate the actual fiber configurations was carried out. Particular care was taken to select the appropriate dimensionless flow parameters to demonstrate that the onset of the ‘‘excess’’ pressure drop due to fluid elasticity is independent of the flow geometry. Employment of this dimensionless group, which is related to the total strain on the macromolecules, yields superior predictions compared to previous results based on the Deborah number. In order to assess the applicability of the results in ideal fiber beds to actual manufacturing processes, flow of viscoelastic fluids through carbon fiber beds was studied under conditions that simulate the autoclave process.