Graphite has a wide application in nuclear industry today. However, the resource of most uranium-graphite reactors in Russia considering their repair-and-renewal operations will be exhausted next 10-15 years. The processing of high-active graphite is made by flameless oxidation method in molten salts. The present work investigates the behavior of radionuclides at flameless oxidation of radioactive graphite in CuO-NaCl-KCl-Na2CO3-K2CO3 multicomponent melt in water vapor. Thermodynamic method of modeling with Terra software was used in this research. This method is an effective and unique one for studying thermal decomposition, reduction and synthesis at various temperatures. The calculations were made using reference database on the properties of individual substances. Graphite burns with the formation of carbon dioxide, methane and condensed potassium carbonate at 573 К. Condensed compounds of cesium, chlorine and uranium evaporate at 1673 К. Temperature rise in the system to 1973 К leads to the evaporation of condensed compounds of beryllium, calcium and strontium. Condensed europium (III) and plutonium (IV) oxides convert into vapor at 2173 К. Condensed nickel oxide evaporates at 2473 К. Further temperature rise to 2773 К leads to the evaporation of condensed americium (III) oxide. The only vapor-gas phase exists in the temperature range 2773-3273 К in the isolated system.