Abstract: The instant invention is directed to shear thickening fluids to prevent unwanted flow in wells penetrating subterranean formations. The shear thickening fluids comprise (1) a water swellable granular clay present in sufficient quantity so that, upon interaction with an aqueous phase, a stiff paste rapidly forms having a strength of at least 2000 lbs/100 ft.sup.2, (2) a nonaqueous phase comprising a hydrocarbon material and a surfactant, and (3) an aqueous phase comprising water and a watersoluble polymer. The granular clay and water-polymer solution are kept separated by the intervening hydrocarbon-surfactant composition, which is the continuous phase. The intervening oil phase prevents the interaction between the water-polymer phase and the granular clay and results in a stable, nonreacting, pumpable composite until such time as the granular clay is fragmented by application of a sufficiently high shear force.