Previously the conditioning of radioactive wastes took place through binding the waste in a matrix of glass, silicon carbide, cement, bitumen, synthetic resin or vitreous carbon. These processes have many disadvantages, particularly the matrix has poor heat conductivity, insufficient resistant to extraction or poor heat resistance and radiolysis effects. A remedy is provided through a carbon matrix in which there is employed as the starting material graphite which is molded with a binder at a temperature above 100.degree. C. There have particularly proven good as the binder sulfur in admixture with nickel powder from which nickel sulfide forms.