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 &PHgr; 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 &PHgr;3 and S-2, and decreases with increasing Z. ¿American Geophysical Union 1991