An intervertebral support device configured to be arranged between two adjacent vertebral bodies (13a,13b) of the spine of a patient in such a way that a relative movement is allowed between said adjacent vertebral bodies (13a,13b) and that said support device can contribute to bear the load of an upper vertebral body on a lower vertebral body, said vertebral bodies (13a,13b) having a sagittal axis and a mid-sagittal plane (π), said adjacent vertebral bodies (13a,13b) having a respective front half (13'a,13'b), a respective rear half (13"a,13"b) and respective edge portions (53a,53b) that face each other, said device comprising a pair of support elements (30,30',40,65',65",70,70'), each support element of said pair having a support surface, said support elements configured to be inserted between said edge portions (53a,53b) of said respective rear half (13"a,13"b) of said adjacent vertebral bodies such that said support surface engages with said edge portions (53a,53b) and assists to bear said load, and said support elements (30,30',40,65',65",70,70') configured to be arranged at opposite sides of said edge portions (53a,53b) with respect to said mid-sagittal plane (π), at respective angles (α) centred on said sagittal axis and measured starting from said mid-sagittal plane (π), said respective angles (α) set between 30° and 90°, characterized in that each support element (30,30',40,65',65",70,70') comprises: - a first longitudinal portion (38a,68a) and a second longitudinal portion (38b,68b), which provide both a support surface portion for said edge portions (53a,53b) of said upper and lower adjacent vertebral bodies, respectively, (13a,13b), said support surface portion of said first longitudinal portion (38a,68a) and said support surface portion of said second longitudinal portion (38a,68a) having a predetermined relative position; - an interface means (39,41,71) between said first longitudinal portion (38a,68a) and said second longitudinal portion (38b,68b) by which a mobility of said relative position is left such that a plurality of use relative positions are allowed according to a shape of said spine corresponding to a position and/or to a movement of said patient, in order to maintain a predetermined anatomic distance between said adjacent vertebral bodies (13a,13b), - a first longitudinal portion (38a,68a) and a second longitudinal portion (38b,68b), which provide both a support surface portion for said edge portions (53a,53b) of said upper and lower adjacent vertebral bodies, respectively, (13a,13b), said support surface portion of said first longitudinal portion (38a,68a) and said support surface portion of said second longitudinal portion (38a,68a) having a predetermined relative position; - an interface means (39,41,71) between said first longitudinal portion (38a,68a) and said second longitudinal portion (38b,68b) by which a mobility of said relative position is left such that a plurality of use relative positions are allowed according to a shape of said spine corresponding to a position and/or to a movement of said patient, in order to maintain a predetermined anatomic distance between said adjacent vertebral bodies (13a,13b),