The spinal prosthetic assembly has a convenient number of elastic intervertebrae prosthetic shock absorbing connectors. These are, according to requirements, either omnidirectional (2a) or directional (2b). The first has two pedicular screw (3a,3b), one fitting the top (4a) and the other the bottom (4b) vertebrae, and anchors (5,6) joined by an omnidirectional dovetail connector (9). The other (2b) has two pedicular screws (14a,14b) fitting the top (15a) and bottom (15b) vertebrae and having anchors (17,18) joined by a directional dovetail connector (18). The omnidirectional prosthetic connecting element has a connector having a hollow cylindrical body cut helicoidally to make it axially elastic and a rectangular spiralled section.; The upper and lower body parts have top and bottom dove tails which are fixed, after bending in situ, on the anchors while the body central hollow part is filled at rest with a visco-elastic shock absorbing fluid. All the parameters of the prosthesis elements are determined and fatigue tested before implanting in the patient.