The work presents the results of studies of the solid-liquid separation processes of different mineralogical and granulometric compositions, different viscosity and concentrations of uranium, zirconium, nitric acid, soda, sodium nitrate. It has been shown that the process of industrial filtration is impossible for finely dispersed phases due to the low separation rate. Requirements for the purity of technological solutions of uranium and zirconium for the extraction process are limited by the technological ability of the filter fabric to retain the smallest particles, including chemical compounds with a particle size of 1–5 μm. The control filtration process is only possible under pressure, for which a new disk press filter was created, which reduced the concentration of the solid phase in the filtrate to 0.06 g/L. For difficult-to-filter suspensions, a screw centrifuge was developed, which ensured minimum sediment moisture after separating the finely dispersed phase from a solution of soda and sodium silicate and created conditions for maximum extraction of zirconium and hafnium from the solid phase. The separation of water-soluble sodium silicate ensured the stability of the process of extraction separation of zirconium and hafnium and made it possible to isolate silicon oxide.