The extraction mixture containing tert-butyl-calix[6]arene, 4-alkyl-2-di-(2-hydroxyethyl)aminomethylphenol and solubilizing additive in dodecane, was proposed for processing of alkaline high-level radioactive wastes. This extraction mixture extracts effectively cesium, strontium, rare-earth elements, americium and plutonium from basic solutions containing up to 8 M sodium salts and 0.1-4 M free alkaline. Acidic solutions could be used for the subsequent stripping of these elements from organic phase. The extraction mixture was tested at "Mayak" PA (Chelyabinsk region). More than 99% of Cs and Sr and about 90% of gross alpha-activity were removed from actual alkaline HLW during the batch test.