Three-dimensional classification of scoliosis is important. However, analyzing large databases of 3D spine models is a difficult and time consuming task. To facilitate this task a method that automatically extracts the most important deformation modes from a set of 3D spine models is proposed. The 3D spine models are first converted into vertebrae relative positions and orientations. Then, a variability model composed of the Fréchet mean and of a generalized covariance is computed. A principal component analysis is applied to that variability model and the extracted components are converted into deformation modes. Those modes are visualized by animating a 3D spine model where the deformation strength varies (for a given mode). The proposed method was applied to a group of 307 scoliotic patients and meaningful deformation modes were successfully extracted. For example, patients' growth, double curves, simple thoracic curves and lumbar lordosis were extracted in the first four deformation modes. Moreover, the obtained deformation modes are not disconnected from conventional surgical classifications since a logistic regression confirmed that there is a statistically significant relation between King's classification and the first four principal deformation modes. The proposed method successfully extracted important deformation modes from a set of 3D spine models and can be used to refine arbitrary classes (King's or Lenke's classes, for instance), thus helping the design of new clinically relevant 3D classifications.