The invention relates to a device for dynamic interlaminar stabilization 1, including: at least one viscoelastic means 14 that serves as a multi-axial shock absorber having a resilient drawback force; a base 10 that is located in the lower portion and made to fit the geometry of the blade of the lower vertebra; a rigid piston 11 that bears on the viscoelastic means 14 and slides through an opening 120 of a hollow cylindrical body 12; a rigid upper hook 13 that is connected to the rigid piston 11 and fits together with the blade of the upper vertebra; and a hollow cylindrical body 12 that serves as a protective cover for the viscoelastic means 14 and the piston 11 and moreover serves as a mechanical safety base for the movement of the upper hook 13. Said means is assembled so as to form the device 1 which becomes a single piece, thus preventing any risk of sliding or disassembly and moreover enabling the ends of the device 1 to always remain attached to the vertebrae while absorbing the mechanical load applied onto the vertebrae. Two devices 1 are paired together, one on each side of the vertebral axis.