The efficiency of 4 samples of alumina catalyst has been studied experimentally in the course of the Claus ’tail gas’ treating processes at the sulphur sub-dew point (TGTP). The samples were characterized by the same chemical and crystallographic composition, the same volume of micropores, the same surface area and the same catalytic activity but differed appreciably in the volume of macropores. An increase in the effective operation time of the catalysts before breakthrough of unrecoverable sulphur containing compounds, with the increasing macropore volume has been established. A theoretical model of the TGTP has been considered and it has been shown that the increase in the sulphur capacity of the catalysts with a larger volume of macropores is due to an increase in the catalysts efficiency factor and a slower decrease in their diffusive permeability during filling of micropores by sulphur.