Abstract: A process for solidifying radioactive wastes by producing compact blocks which are to be disposed in transporting or permanent storage containers. The compact blocks are produced from prefabricated ceramic tablets which contain radioactive substances and a matrix which continuously surrounds these ceramic tablets and is solid in its final state. Glass powder or a mixture of oxidic non-clay minerals or a mixture of both is used as the matrix material. The ceramic tablets and the matrix material are filled into the container and are compressed. The resulting compressed mixture is heated to a temperature in the range from 1423.degree. K. to 1623.degree. K., is held at this temperate range for one to three hours, and is finally gradually cooled to room temperature.