Due to the low permeability and high ductility of rock salt, many salt diapirs, such as those in Germany and the Netherlands, are targeted as long-term repositories for disposal of high-level radioactive and chemical wastes. Geophysical and subsurface data show that the Gorleben salt diapir, which is one of the most extensively investigated diapirs in the world, and other salt diapirs of the Zechstein Formation in Germany contain large blocks (∼80 m thick) of high-density anhydrite inclusions. These blocks, which were carried upward by the rising salt, are considered to be detached segments of intercalated layers that initially were deposited with the salt. Results of physical and numerical models, presented here, show that such detached, high-density blocks, which were entrained and carried upward by the diapir at an earlier stage, tend to sink in the late stages of diapiric evolution when the rate of diapiric rise slows down. During their descent, these high- density competent blocks deform by folding and create shear zones at the immediate contact with the less competent salt. The descending blocks initiate a secondary internal flow within the salt diapirs they descend, and they may deform any repository built within such diapirs, which would otherwise be considered as tectonically inactive.