A method is presented to solidify radioactive waste liquids such as washing liquids containing radioactive material generated in an atomic power plant to thereby facilitate transport of them. A drum can is inserted into a drum can supporting vessel and carried by a truck toward and under the evaporation chamber. A lifter is upwardly extended by an elevator to provide an intimate contact between the lower end of a steam chamber and the upper end of the drum can through a seal ring. Next, a mixture of a washing waste liquid and a defoaming agent is filled from a supply pipe into the drum can in spraying manner. Into a heater is supplied heated vapor from a heated vapor supply pipe to vaporize and condense the waste liquids. The vaporized vapor passes through a demister and is condensed by a condenser. After the condensed liquids of a predetermined concentration have been obtained, a lifter is retracted to cause the drum can to be moved under a cement mixer to feed cement into the drum can for mixing and solidifying it therein.