The capillary model of Comiti and Renaud (1989) is applied to high voidage beds composed of spheres and fibers. Both the linear and non-linear laminar flow regimes are tested. In the case of sphere beds, it clearly appears that the applicability range of the model depends on porosity, as has been commonly stated, but also on the Reynolds number for the non-linear laminar flow regime. This latter point has not been observed in other previous published works, because the variation of tortuosity with porosity was:often neglected. Consequently, we assume that in high voidage beds of spheres and for low Reynolds numbers, the fluid flow is not of channel type, as disturbances generated by particles are strong. This phenomenon is weaker when the Reynolds number increases, which again leads to channelling of the fluid. For fibrous mats? no dependence on Reynolds number is observed and the applicability of the capillary model is well defined by bed porosity, for the investigated range of Reynolds number. We should notice that this range is more limited than that tested for sphere beds. When the capillary model cannot be used, it may be interesting to develop a model based on the how around submerged objects.