The combined effects of hindered diffusion and adsorption in a single pore can be used as the basis for modeling diffusion and adsorption of macromolecules such as proteins in porous media. We examine here the influence of pore tapering, which affects both the hindrance and adsorption effects on the overall transport rate. The governing equation is developed by averaging the continuum diffusion equation across the pore, and it is solved numerically for the case of a cylindrical pore with radius decreasing linearly with axial position. The effect of the taper on axial concentration profiles is to give rise to a pronounced inflection relative to the shape seen for a straight pore, and the net uptake rate is altered as well. These results indicate that extraction of pore structure details from solute uptake information is problematic, and that empirically correlated pseudocontinuum transport models may be more reliable.