Intervertebral disc prosthesis including two plates (2, 3) intended to be anchored to the respective vertebrae, and an intermediate damping core placed between these two plates (2, 3), this intermediate core comprising a first shell forming an articular surface for cooperating with a conjugate articular surface possessed by a first plate, and a flexible element placed between this first shell and a part (5; 2) for receiving this core, said first shell and said receiving part (5; 2) comprising means (18, 26) for guiding their mutual movement for bringing them closer or moving them away from each other, made possible by the flexibility of said flexible element; - said receiving part (5; 2) comprises a cavity intended to receive the flexible element, this cavity being delimited by a first peripheral wall and by a bottom wall, said first peripheral wall having an external peripheral face; and - said first shell has a second peripheral wall forming an internal face, this internal face, when said first shell and the receiving part (5; 2) are in their assembling condition, coming into close proximity to said external peripheral face and being able to slide along the latter; said cavity is intended to snugly receive the flexible element; characterized in that: - said cavity which said receiving part (5; 2) comprises, has an undercut shape, i.e. it has an opening for introducing the flexible element with a smaller section than the section which this cavity has underneath this opening, said flexible element being deformable so as to be able to forcibly cross the edge of said first peripheral wall delimiting this opening; - said flexible element comprises a third peripheral wall intended to be placed along the internal face of said first peripheral wall of the receiving part (2; 5), a first end face connected to this third peripheral wall and a housing opening into its second end face, opposite to said first end face; said housing comprises an undercut shape, i.e. it has an opening with a smaller section than the section which this housing has underneath this opening; and - said first shell has a stud suitable for being snugly placed in this housing, this stud having, at its free end, a larger section than the one which it has at its base, and said flexible element being deformable so that this stud is adapted to forcibly cross the edge of said third peripheral wall of the flexible element delimiting said opening. - said receiving part (5; 2) comprises a cavity intended to receive the flexible element, this cavity being delimited by a first peripheral wall and by a bottom wall, said first peripheral wall having an external peripheral face; and - said first shell has a second peripheral wall forming an internal face, this internal face, when said first shell and the receiving part (5; 2) are in their assembling condition, coming into close proximity to said external peripheral face and being able to slide along the latter; - said cavity which said receiving part (5; 2) comprises, has an undercut shape, i.e. it has an opening for introducing the flexible element with a smaller section than the section which this cavity has underneath this opening, said flexible element being deformable so as to be able to forcibly cross the edge of said first peripheral wall delimiting this opening; - said flexible element comprises a third peripheral wall intended to be placed along the internal face of said first peripheral wall of the receiving part (2; 5), a first end face connected to this third peripheral wall and a housing opening into its second end face, opposite to said first end face; said housing comprises an undercut shape, i.e. it has an opening with a smaller section than the section which this housing has underneath this opening; and - said first shell has a stud suitable for being snugly placed in this housing, this stud having, at its free end, a larger section than the one which it has at its base, and said flexible element being deformable so that this stud is adapted to forcibly cross the edge of said third peripheral wall of the flexible element delimiting said opening.