The mathematicaldescription of the process of solution purification from heavy metal ionsby means ofion exchange inan apparatus with continuous suspended layer was developed. At the developing mathematical description the following assumptions were used: the ionite is monodisperse and has a spherical shape, uniform initial distribution of substances in the ionite, the ion exchange equilibrium is described by Henry equation, the velocity of the process is limited by both internal and external diffusion, the ionite in the device moves with longitudinal mixing effect, kinetic and hydrodynamic process parameters are constants. Mathematical description includes the following equations: the diffusion equation of ionite, isotherm equation ion exchange, the equation for average concentration of the substance in the ionite, equations of the one-parameter diffusion model, initial and boundary conditions. To solve boundary value problem, we use the integral Laplace transformmations. The obtained equation allows calculating the solution concentration at the output of the apparatus. The authors determined the validity of the mathematical model on the example of the water purification from zinc ions on the KU-2-8 cationite in the continuous single-chamber apparatus with a fluidized bed. The ion exchange unit has a cylindrical body with a diameter of 0.08 m and a conical bottom. Distributive lattice with thickness of 3×10-3 m and with holes with diameter of 2×10-3 m and orifice of 20.6 % were located in the lower part of the device. The height of the fluid-bed ionite layer in the device was 0.12 m. The chamber for separation of ion exchanger and solution was placed in the top of the device. This chamber had a cylindrical shape with a diameter of 0.15 m and height of 0.1 m. The chamber for fluid-bed ionite and chamber for separation of ionite and solution were joined conical shell. The solution flow rate in the apparatus was 2.1×10-5 m3/s. The ionite flow rate in the device was 1.42×10-7 m3/s. The initial concentration of the solution of zinc chloride was taken 5.1×10-3 kg-eq/ m3. The concentration of zinc ions in the spent ionite was 0.67 kg-eq/m3. The concentration of zinc ions in the purified solution was 6.4×10-4 kg-eq/m3. The calculated value of concentration of zinc ions in the spent ionite was 0.66 kg-eq/m3. The calculated value of concentration of zinc ions in the purified solution was 7.2×10-4 kg-eq/m3. The deviation of the calculated results from the experimental data does not exceed 12 %. The elaborated mathematical model is recommended for practical application. For citation:Natareev S.V., BykovА.А., Zakharov D.E., Nikiforova T.E. Ion-exchange in fluid-bed device of continuously working. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2017. V. 60. N2. P. 85-90.