The aim of this report is to focus on competitive sorption of strongly basic anion-exchange resin (BO020) in model solutions similar to on-site sulfuric acid solutions obtained by leaching the Uch-Kuduk deposit ores. The BO020 resin was applied to a modeling study of the uranium and competitive ions sorption in sulfuric acid solutions at pH = 1.2 and a concentration of 7 g/l of sulfate ions. The chemical composition of the salt solution after sulfuric acid ore leaching was as follows: U6+ - 0.1-0.5 g/L; Fe3+ - 0.07-0.7 g/L , Fe2+ - 0.07- 0.7 g/L; SO42- - 7.0 - 13.0 g/L; P5+ - 0.08-0.2 g/L; Cl- - 0.15 - 0.3 g/L; Si4+ – 0.085 - 0.3 g/L; Al3+ - 0.01 - 0.164 g/L, Ca2+ - 0.5 - 0.7 g/L. The BO020 resin has fairly high uranium uptake and sorption capacities, but phosphorus, iron, aluminum, and manganese sorption capacities are very small. The nitrate and chloride ions have high sorption capacities only at high concentrations in solution. The results can be used to make the best choice of ion exchanger application for underground leaching of uranium.