The study of the morphology of the human spine has attracted research attention for its many potential applications, such as image segmentation, bio-mechanics or pathology detection. However, as of today there is no publicly available statistical model of the 3D surface of the full spine. This is mainly due to the lack of openly available 3D data where the full spine is imaged and segmented. In this paper we propose to learn a statistical surface model of the full-spine (7 cervical, 12 thoracic and 5 lumbar vertebrae) from partial and incomplete views of the spine. In order to deal with the partial observations we use probabilistic principal component analysis (PPCA) to learn a surface shape model of the full spine. Quantitative evaluation demonstrates that the obtained model faithfully captures the shape of the population in a low dimensional space and generalizes to left out data. Furthermore, we show that the model faithfully captures the global correlations among the vertebrae shape. Given a partial observation of the spine, i.e. a few vertebrae, the model can predict the shape of unseen vertebrae with a mean error under 3 mm. The full-spine statistical model is trained on the VerSe 2019 public dataset and is publicly made available to the community for non-commercial purposes.