The article provides the fundamental possibility of the associated extraction of Rare Earth Metals during carbonate conversion of phosphogypsum and red muds. There are the isotherms of solubility of carbonates, phosphates and hydroxides of europium, neodymium, holmium, cerium, and ytterbium obtained in carbonate solutions. By changing the carbonation conditions, Rare Earth Elements are transferred to a carbonate solution in the form of water-soluble complexes. Then they can be recovered by precipitation. Also, there were found the optimum conditions with the maximum degree of recovery into the solution.