Fluorine or a fluorine compound is subjected to a reaction with a spent oxide fuel to produce fluorides of uranium and plutonium, and recovering the fluorides using a difference in volatility behavior. The method includes steps of: subjecting a mixture of UO.sub.2 and PuO.sub.2 with hydrogen fluoride mixed with hydrogen to HF-fluorinate uranium and plutonium into UF.sub.4 and PuF.sub.3; subjecting UF.sub.4 and PuF.sub.3 with a fluorine gas to F.sub.2-fluorinate uranium and plutonium into UF.sub.6 and PuF.sub.6; and fractionating UF.sub.6 and PuF.sub.6 using a difference in phase change of obtained UF.sub.6 and PuF.sub.6, removing a part of UF.sub.6, and volatilizing the remaining UF.sub.6 and PuF.sub.6 at the same time. By such a reprocessing method, PuF.sub.4 hard to undergo a reaction is prevented from being formed as an intermediate fluoride, the material of a reactor is hard to be corroded, and a consumption of expensive fluorine gas is reduced.