A vertebral support device ( 1 ) is disclosed, which in various embodiments comprises at least two osseous anchoring implants ( 2 ), each designed to be anchored to a vertebra, and at least one linking element ( 3 ) fixed to the osseous anchoring implants ( 2 ) by fasteners ( 20 ) that maintain a fixed angle between the longitudinal axis (L) of the linking element ( 3 ) passing through rigid elements ( 34 ) of the linking element ( 3 ) and the insertion axis (DV) of the implants ( 2 ). The linking element ( 3 ) includes at least one elastic dampening element ( 31 ) that that allows the implant-bearing vertebrae some freedom of movement. The dampening element ( 31 ) accommodates the stresses imposed on the linking element ( 3 ) during movement of the vertebrae and tends to return the support device ( 1 ) to its normal configuration.