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The paper deals with equilibrium and kinetics of rhenium sorption using AMR weak-base anionite from simulated sulfuric solutions with high and low acidity. A comparative analysis was carried out for Freundlich, Langmuir and Sips sorption models. It was found out that equilibrium experimental data fitted with the highest determination factor by the Sips equation from solutions with high acidity and by the Henry one for low acidic solutions. A comparative analysis was carried out for sorption kinetics using different kinetic models; the values were estimated for calculated effective factors of intra-particle diffusion and model approximation to experimental data. To assess the contribution of chemical interaction in the rhenium sorption process, kinetics data were quantitatively approximated using pseudo-first order, pseudo-second order and Elovich kinetic models. It was found that the pseudo-second order model fits experimental data most accurately. Results were given on rhenium stripping by ammonia solution. The results obtained may be used for rhenium recovery from washing sulfuric acid in the systems of wet dust and gas scrubbing during pyrometallurgical processing of copper ore concentrates and other acidic industrial solutions as well as liquors after uranium sorption.