A sealed and insulating reservoir to contain a pressurized cold fluid, the reservoir comprising: a sealed rigid enclosure (4), a sealed membrane (1) intended to be in contact with the cold fluid contained in the reservoir, an insulating barrier (3) positioned between the sealed membrane and the internal surface of the rigid enclosure, the insulating barrier forming a supporting surface to support the sealed membrane, and a pressure‑equalizing device (5) able to limit the pressure differential between a first sealed volume (2) situated on the inside of the sealed membrane and a second sealed volume (3) situated on the outside of the sealed membrane.