Internal filtration in slurry bubble columns offers a possible solution to the filtration problems related to this reactor type. The applicability of the concept has already been demonstrated at full-scale for wastewater treatment, even though a theoretical description of internal filtration is lacking. Two types of hydrodynamic models were developed for a filtering slurry reactor. Both the model of the surface renewal type and the model based on a force-balance approach predict that the solids concentration at the axial position of the filter uniquely depends on a single novel dimensionless number. The validity of these theories was demonstrated by measuring filter-cake resistance as an indirect measure of solids concentration for a system in batch operation with respect to solids. In the experiments the load of solids, permeate flux (J), superficial gas velocity (U-g), particle diameter (d(p)), kinematic liquid viscosity (v(l)), and molar mass of the gas were varied.