Physical and chemical regularities of sorption extraction of scandium and yttrium compounds from (0.1–2.5)∙10-4 M aqueous solutions by zirconium-silica nanosorbent with specific surface area of 900-1000 m2/g, pore radius of 3.5-7, 6 nm and with a ZrO2 content of 29% have been established. It is shown that the studied sorbent efficiently (>99%) removes scandium and yttrium at pH 8 – 10 (Sc) and pH 9 – 10.5 (Y) and at sorbent consumption of 0.4 g/dm3. The time to reach sorption equilibrium is 240 min (Sc) and 210 min (Y). Modeling of scandium and yttrium sorption kinetics by Boyd’s external diffusion and internal diffusion models shows that sorption takes place in a mixed diffusion mode. The values of sorption rate constants (0.018 min-1 Sc, 0.033 min-1 Y), external mass transfer constants (4.74 ∙ 10-8 m/min Sc, 8.51 ∙ 10-8 m/min Y) and internal diffusion rate constants (0.0099 min-1 Sc, 0.0093 min-1 Y) have been calculated. It is established that the kinetics of sorption follows the pseudo-second-order model. It is shown that the sorption isotherms of both investigated metals are described by Freundlich, Frumkin-Fowler-Guggenheim and Dubinin-Radushkevich models. The constants of sorption isotherm models, characteristic energy of sorption (10.79 kJ/mol Sc, 9.58 kJ/mol Y), ΔG0 of sorption (-32.82 kJ/mol Sc, -30.77 kJ/mol Y) are calculated. The results of calculations indicate a significant affinity of scandium and yttrium compounds for this sorbent, spontaneous nature of the process and mixed nature of sorption with a predominance of chemisorption, a significant contribution of ion exchange to the sorption mechanism.