Highly radioactive material is permanently disposed of by first forming a borehole by a metal fusion drilling method with a metal lining from a casting continuously formed from a metal melt and then depositing the highly radioactive material for final storage in a lower area of the lined borehole. This lining is melted locally immediately above this lower area after deposition of the material to separate the lower area holding the material from the rest of the lining and permit this lower area and the material held therein to migrate automatically downward toward the center of the earth. To promote this downward migration, the wall thickness of the metallic lining of the lower borehole region has a wall thickness that increases from the top downward and on the lower area is formed with a downwardly directed conical tip.