Methods for spinal stabilization operative to prevent lateral bending, extension, and rotation across two or more adjacent vertebrae are described. Broadly, the method includes placing two or more anchors at each vertebral level, passing one or more sutures through each anchor at each level, applying tension to the sutures and joining the sutures in a cross-braced arrangement over the disc space between two or more vertebrae to prevent lateral bending, extension, and rotation of the spinal segment. The sutures can be welded in any combination of diagonal and vertical patterns across the adjacent vertebrae. In some embodiments, two or more sutures can be threaded through some of the suture anchors such that multiple vertebral levels can be joined in a cross-braced arrangement. Two or more sutures can also be used in multiple anchors in two adjacent vertebrae to provide additional reinforcement or stabilization across different portions of the two vertebrae. The sutures reinforcing different portions of the vertebrae can have different breakage strength and different elastic properties. The invention may be used on the cervical, thoracic, lumbar, or sacral regions of the spine.