The optimal conditions for the nitric acid dissolution of precipitates of hydroxides and hydrated oxides of rare-earth elements, uranium, and thorium obtained after autoclave alkaline opening of samples of monazite concentrate have been determined. The distribution of radioactive impurities between the solid phase and the solution in the processes of alkaline opening, dephosphorization, and acid dissolution of the pulp was studied. Two options are proposed for the extraction of uranium and thorium in the presence of rare earth elements, followed by separation of the components using tributyl phosphate of various contents in the carbon diluent.