Rapid development of nuclear engineering, medicine and radiation technologies is accompanied by increase of the radioactive waste (RAW) including long-lived ones. A RAW handling assumes their element content and activity analysis (characterization), compacting and disposal. This problem is of ultimate importance after shutdown of Chornobyl nuclear power plant Unit 4. The activity of the RAW inside the unit is estimated as much as 20 MCi (mainly on account of the Cs-137). These circumstances ensure a necessity of elaboration of the especial methods for express-analysis of large RAW fluxes. An immobilization of the long-lived radionuclides is entailed in turn with the problem of their localization into stable matrix as well as placing in resistive to radiation containers and geological structures. The report contains an overview of methods elaborated in NSC KIPT for RAW characterization and investigation using the bremsstrahlung of the high-current electron accelerator of radiation stability of the artificial and natural barriers for radionuclide immobilization.