An improved method of disposing of radioactive or hazardous liquid aqueous waste compositions having a substantial amount of dissolved solids comprises mixing the liquid under a high mechanical shear with a clay selected from the group consisting of attapulgite, sepiolite, and mixtures thereof. Water soluble or miscible organic liquids as well as liquid hydrocarbon mixtures thereof may also be solidified by utilizing the aforesaid clays together with an organic ammonium montmorillonite having at least 10 carbon atoms, the amount of montmorillonite used being proportional to the amount of liquid hydrocarbon present.