Abstract: A storage device has an inner enclosure (6) and a leakproof and a rigid outer enclosure (5), which are mounted one inside the other and separated by an intermediate space (9) containing a fluid, continuous in phase at pressures other than that of the material stored, and pressure measurement equipment (16, 15) enabling the differences in the pressure of the fluid to be monitored. Advantageously, the device additionally features sampling equipment (18, 17) enabling the composition of the fluid to be monitored. The device may be buried, the outer enclosure being then placed against the cement walls (4) of a cavity, which may be a drilled well. The inner enclosure may feature a leakproof skin which is made rigid by the presence in the intermediate space of a porous and rigid filling material in which the fluid can circulate.