Specimens of reconstituted clay were contained under vertical pressure in a 250 mm diameter cylindrical test cell fitted with a peripheral drain. Using a self-boring device, a 35 mm diameter cavity was formed in the centre of each specimen, and outflow permeability tests were performed to simulate possible in situ test procedures. Either the cavity extended over the whole specimen height and radial flow conditions prevailed, or the cavity was shorter and a steel lining was progressively withdrawn to induce both vertical and radial flow. Generally, the cavities were observed to degrade and partially fill with softened material, yet the measured permeabilities were higher than expected on the basis of other information. Pore water pressure measurements suggested that hydraulic fracturing was taking place around the cavities, even though applied pressure heads were very small. Fractured material is then thought to have fallen into the cavities. In specimens containing silt layers, the cavities did not degrade so much, and more satisfactory permeability measurements proved possible. The results suggest that the assumption of a stable cavity, necessarily made when interpreting some in situ tests, may not be justified.