This prosthesis (1) includes two plates and an intermediate damping core (4) placed between both of these plates, this core (4) comprising a first shell (6) and a flexible element placed between this first shell (6) and a part for receiving the core. The first shell (6) and the first receiving part include means (18, 26) for guiding their mutual movement for bringing them closer or moving them away from each other. According to the invention, the receiving part includes a cavity intended to snugly receive the flexible element. The cavity being delimited by a first peripheral wall and by a bottom wall. The first peripheral wall having an external peripheral face; and the first shell (6) has a second peripheral wall forming an internal face. The internal face, when the first shell (6) and the receiving part are in their assembling condition, coming into close proximity to said external peripheral face and being able to slide along the latter.