An industrial dyeing process in supercritical carbon dioxide has been modelled with computational fluid dynamics using Ansys Fluent software. In order to investigate the distribution of the dye carrier fluid, the flow resistance of the fabric has been accurately characterised. For this purpose, in the first part of the work a plain-woven fabric geometry was created in the open software Tex-Gen and modelled in Ansys Fluent to predict the permeation of fluid through the pores of the fabric material and to estimate the relationship between local fluid velocity and pressure drop. The second part of the study focused on evaluating the influence of beam structure, inlet flow rate, fabric height on the fluid flow through the fabric, which must be uniform to achieve a homogeneous level of dyeing. From the simulations the main obstacle to achieving a uniform flow velocity in the fabric is the pressure rise that occurs in the beam and creates a slight difference in permeation velocity between the two axial ends of the fabric; other disturbances, such as the effect of the perforated structure of the beam, are usually minor. Due to the low viscosity of supercritical carbon dioxide, inertial losses predominate over viscous losses in the porous medium. This means that approaches based only on the permeability of the fabric and the application of Darcy's law are inadequate to correctly predict the response of a dyeing unit when using carbon dioxide.