The present invention relates to a treatment of high-level waste of radiochemical production containing radionuclides and macro-admixtures including sodium. The method of extraction of radionuclides by processing acidic aqueous waste solutions by extractants containing macrocyclic compounds selected from the group of crown ethers having aromatic fragments containing alkyl and/or hydroxyalkyl substituents of a linear and/or branched structure, and/or cyclohexane fragments containing alkyl and/or hydroxyalkyl substituents of a linear and/or branched structure, and/or fragments of —O—CHR—CH2O—, where R is the normal or branched alkyl or hydroxyalkyl in organic solvents containing polyfluorinated telomeric alcohol 1,1,7-trihydrododecafluoroheptanol-1 having the formula H(CF2CF2)nCH2OH, where n=3, and a mixture of polyoxyethylene glycol ethers of synthetic primary higher aliphatic alcohols of a fraction C12-C14 of a general formula CnH2n+1O(C2H4O)mH, where n=12-14, m=2 is proposed. A possibility of selection of quantitative and qualitative composition of the extractant depending on the waste composition and the object to be achieved of joint or individual extraction of radionuclides results in universal technology. A method of regeneration of extractants containing crown ethers allowing one to carry out the operation of extraction of radionuclides in a commercial scale under countercurrent dynamic conditions, with regeneration of the extractant for reuse is also proposed.