A device for stabilizing at least a portion of the spinal column, including a longitudinal member sized to span a distance between at least two vertebral bodies and being at least partially formed of a shape-memory material exhibiting pseudoelastic characteristics at about human body temperature. A number of bone anchors are used to secure the longitudinal member to each of the vertebral bodies. The longitudinal member is reformed from an initial configuration to a different configuration in response to the imposition of stress caused by relative displacement between the vertebral bodies, and recovers toward the initial configuration when the stress is removed to thereby provide flexible stabilization to the spinal column. During reformation of the longitudinal member, at least a portion of the shape-memory material transforms into stress-induced martensite. In a particular aspect of the invention, the longitudinal member is a plate having a central portion at least partially formed of the shape-memory material, and a pair of connection portions disposed at opposite ends of the central portion for connection to each of the vertebral bodies. The central portion of the plate defines a number of alternating ridges and grooves along a length thereof having an initial amplitude corresponding to the initial configuration and a different amplitude corresponding to the different configuration.