Graphical Abstract: The effect of sulphuric acid concentration on solvent extraction of ReO4- by the long-chain aliphatic tertiary amines and alcohols in a wide range of H2SO4 concentrations in initial solutions is discussed. It has been established that the influence of the sulphuric acid concentration on rhenium solvent extraction is largely due to the extraction process mechanism. In the case of the anion-exchange mechanism, ReO4- is best extracted from weakly acidic solutions, whereas when the hydrate-solvate mechanism takes place – from solutions containing 4-7 mole/l H2SO4.