Medical image analysis is of great importance for understanding human body anatomy, disease diagnosis, and patient treatment. Compared to the general computer vision tasks, most anatomical structures (e.g. heart, bones) are embedded with very unique shape information. The information presents not only the geometric correlation between structures, but also various pathologies. In the proposal, we address the task of medical image analysis using machine learning methods together with the geometrical shape priors. The geometrical priors have different expressions (global priors, and local priors), according to the specific scenarios. Several practical applications, such as motion reconstruction of left ventricle wall, femur parsing, and spine labeling, are discussed to demonstrate the usage of geometric shape priors together with machine learning techniques. The geometric priors validated by the experimental results help achieve the significantly better analytical results.