Methods and apparatus for sealing a well are disclosed. The method includes introducing a plug axially into the well, with a mouth of the plug turned up and a bottom wall part turned down, the plug being positioned in the well at a desired depth. The plug is inflated by injecting a high-pressure liquid into it via its mouth so that a tubular wall part of the plug expands radially beyond its elastic limit and presses firmly and tightly against the wall of the well by a crimping effect, while its bottom wall part serves as a sealing partition, forming a tight barrier between lower and upper parts of the well that it separates. The plug has an internal axial mandrel that connects its mouth to its bottom wall, the mandrel being pierced with channels that allow injection of high-pressure liquid inside the plug via the mouth and channels.