Compressive fracture of osteoporotic vertebrae has been one of the most important health problems in aged societies because severely injured spin might be a reason of bedridden for elderly people. Osteoporosis has been widely assessed by averaged bone mineral density of vertebrae measured using DEXA, however, BMD sometimes does not reflect the strength of vertebrae. CT imaged based finite element method (CT-FEM) has been applied to evaluate the strength of vertebrae based on the biomechanics theory and approved by a part of the highly advanced medical treatment in Japan. In the present study, compressive strength of more than 100 vertebrae were evaluated using CT-FEM, and the correlation between BMD and the strength was thoroughly investigated. It was found that some vertebrae with high BMD could have low strength which may cause fracture easily. Thus, a controversial point of the BMD based diagnosis of osteoporosis was clearly indicated. In this invited talk, some basic theories of CT-FEM and fracture assessment and some key results from the recent study will be presented.