The paper provides the results of experiments on the hydrometallurgical processing of finely dispersed technogenic raw materials for primary aluminum production in Soderberg cells (case study of the Irkutsk Aluminum Smelter) – aged sludge. The components of this sludge are dust from electrostatic precipitators (79.7 %), wet gas cleaning sludge (4.4 %) and coal froth flotation tailings (15.8 %). According to the grain-size analysis carried out, aged sludge sample particles have a size of –50 μm. According to the chemical composition analysis of the sludge sample, main components in it are carbon, cryolite, chiolite with a small amount of other compounds (corundum, ralstonite, spodumene, fluorite). Fluorine leaching experiments were carried out with a 2 % sodium hydroxide solution at a stirrer speed of ~1020 rpm. Using the mathematical planning of a three-factor experiment, it was found that the maximum concentration of fluorine in the solution (15.844 g/dm3) is achieved with the following optimal parameters of fluorine alkaline leaching: temperature of 90 °C, liquid-to-solid ratio of 9 : 1, and time of 90 min. The multidimensional polynomial equation was obtained for fluorine alkaline leaching from aged sludge. Cryolite was obtained from fluorine-containing solutions (by the reaction of sodium fluoride interaction with sodium bicarbonate and an aluminate solution), which was confirmed by X-ray phase analysis data.