The invention relates to the technology of recovery of rare-earth elements form both solid fossil and technology-related materials obtained by means of their target-oriented processing. Rare-earth elements recovery method include the acid leaching of ground to less than 100 μm solid fossil and technology-related materials with the mixture of sulphuric and nitric acid at ratio from 6:1 to 1:1 mass parts, at the concentration in mixture of acids less than 15 wt. % at liquid/solid phases ratio of L:S from 2:1 to 6:1 mass parts. During the leaching operation progress the vacuum-impulse action is conducted during all operation of transferring of rare-earth elements compounds into a solution and obtaining of a precipitate of remained solid fossil and technology-related materials. The obtained precipitate of solid fossil and technology-related materials is separated from leaching solution.Separation of rare-earth elements from leaching solution is conducted using ion-exchange filter or membrane filter.