Abstract: Method for the solidification, in a manner which protects the environment against contamination, of waste materials obtained during reprocessing of irradiated nuclear fuel and/or breeder materials in a matrix of borosilicate glass. Highly radioactive solutions or slurries containing the waste materials in dissolved or suspended form are evaporated in a vessel in the presence of glass former substances until they are dry, the dry residue is calcinated and the calcinate is melted together with the glass formers while the waste gases are discharged to the environment. The waste liquid is obtained from a reprocessing system without pretreatment, is mixed with glass formers and a reduction agent and then is introduced in a controlled, continuous manner into the center of a borosilicate glass melt disposed in a melting crucible at a temperature in the region of 1000.degree. to 1400.degree. C.