Storage tank for a cryogenic fluid comprising an inner tank that is configured to store said fluid and that is seated in an outer envelope, the inner tank and the outer envelope having a shared longitudinal axis, such that a thermal insulation volume surrounds the inner tank, and that said outer envelope surrounds said volume about the inner tank, said tank being such that: - at least one damping element made of a deformable material is inserted between one end of said inner tank and said outer envelope to wedge the inner tank against the outer envelope, - the shared longitudinal axis of said inner tank and said outer envelope defines a direction X, - said damping element is fastened firstly to said end of the inner tank and secondly to said outer envelope, and is arranged to create said wedge by positioning said end of the inner tank in relation to said outer envelope when said end of the inner tank moves in translation along the direction X, and - first fastening means are arranged to attach said damping element to the end of said inner tank and second fastening means are arranged to attach said damping element to an inner surface of said outer envelope, characterized in that said damping element is ring-shaped, and said first fastening means comprise a sleeve (140a, 140d) fastened to the end of the inner tank and have a first shoulder and a thread that are configured to fasten said damping element about a portion of said sleeve (140a, 140d), against said first shoulder, and to hold said damping element against said first shoulder by tightening an assembly comprising a washer and a nut onto said sleeve portion, and in which said second fastening means comprise a neck formed about an opening at one end of the outer envelope positioned on the same side of the tank as the end of the inner tank, and - the neck has a second shoulder, and a locking ring crimped onto said neck and configured to hold said damping element against said second shoulder, or - the inner surface of the neck has a slot into which a ring-shaped metal insert is inserted, or a threaded hole into which the ring-shaped metal insert is screwed, the inner surface of said insert having a second shoulder and a thread that are arranged to hold said damping element against said second shoulder by tightening an assembly comprising a washer and a nut in said ring-shaped metal insert. - at least one damping element made of a deformable material is inserted between one end of said inner tank and said outer envelope to wedge the inner tank against the outer envelope, - the shared longitudinal axis of said inner tank and said outer envelope defines a direction X, - said damping element is fastened firstly to said end of the inner tank and secondly to said outer envelope, and is arranged to create said wedge by positioning said end of the inner tank in relation to said outer envelope when said end of the inner tank moves in translation along the direction X, and - first fastening means are arranged to attach said damping element to the end of said inner tank and second fastening means are arranged to attach said damping element to an inner surface of said outer envelope, characterized in that said damping element is ring-shaped, and said first fastening means comprise a sleeve (140a, 140d) fastened to the end of the inner tank and have a first shoulder and a thread that are configured to fasten said damping element about a portion of said sleeve (140a, 140d), against said first shoulder, and to hold said damping element against said first shoulder by tightening an assembly comprising a washer and a nut onto said sleeve portion, and in which said second fastening means comprise a neck formed about an opening at one end of the outer envelope positioned on the same side of the tank as the end of the inner tank, and - the neck has a second shoulder, and a locking ring crimped onto said neck and configured to hold said damping element against said second shoulder, or - the inner surface of the neck has a slot into which a ring-shaped metal insert is inserted, or a threaded hole into which the ring-shaped metal insert is screwed, the inner surface of said insert having a second shoulder and a thread that are arranged to hold said damping element against said second shoulder by tightening an assembly comprising a washer and a nut in said ring-shaped metal insert.