This extension study will only enroll individuals who have completed one year of treatment in the parent protocol "Effect of Teriparatide, Vibration and the Combination on Bone Mass and Bone Architecture in Chronic Spinal Cord Injury (NCT01225055)". This study will allow those individuals who received Teriparatide (20ug/day) and vibration (10 min/day) during the parent study to be treated for a second year and will allow those individuals who received teriparatide-placebo to have the opportunity to have a full year of teriparatide therapy. This study will determine if two years of exposure to teriparatide will result in a greater increase in Bone Mass Density (BMD) than that seen after a single year's treatment. Subjects will be evaluated at 6 and 12 months after initiating treatment with measurement of bone density as well as bone markers of formation and resorption.