Spinal stabilization mechanisms act to prevent lateral bending, extension, and rotation across adjacent vertebrae. Methods for spinal stabilization includes placing one or more anchors at each vertebral level, positioning one or more sutures around each anchor at each level such that the each suture forms a loop or band around two adjacent anchors, applying tension to the ends of each suture to tighten the suture loop around the anchors and welding overlapping ends of each suture together to form suture bands connecting the anchors and thereby preventing lateral bending, extension, and rotation of the spinal segment. A suture banding tool may be used to place the sutures around the anchors in a looped configuration, apply tension to the suture ends to tighten the suture loop around the anchors and weld the ends of the suture to form a suture band connecting the anchors. The suture banding tool includes a suture welding tool having opposing jaws having a gap therebetween for receiving a portion of a suture and a heating element for welding the suture, a suture holding device releasably attached to the suture welding tool having at least one recess for holding a portion of a suture in a looped configuration, and one or more sutures.