We examine the permeability of a medium with thin tapered cracks to a single‐phase fluid flow in the presence of immobile matter which is accumulated in the tips of cracks. The original Kozeny‐Carman relation shows an increase in permeability of such a material relative to the case when tips are free of accumulated matter. To resolve this paradox we introduce a corrected version of the Kozeny‐Carman relation for the case when the shape of a crack cross‐section can be described by a power law. This class of crack shapes includes the important cases of triangular cracks and space between two contacting circular grains. The revised relation includes the original porosity Φ and specific surface area S of the material without accumulated matter as well as the degree of filling a crack space by accumulated matter Z. The permeability is proportional to Φ3 and S−2, and decreases with increasing Z.