<p>We aim to understand the mechanism that forms the shapes of bones. Biological studies suggest that bone morphology is adapted to the external loads. To explain how the external loads affect bone morphogenesis, the mathematical models have been developed using topology optimization. Using these mathematical models, the structure like trabeculae can be generated. However, the formation of external shapes of bones has rarely been studied. Because the inner structure and the external shape of bones are formed by the same types of cells, we hypothesize that the formation of external shape also depends on the external loads and can be explained by topology optimization. The vertebral body of fish we focus on exhibits the various shapes and its morphology seems to be closely related to the swimming mode of fish. To reveal the relationship between the vertebral shapes and the external loads, we built a mathematical model using topology optimization. By setting the different loadings expected to occur during swimming of fish, the model can produce the shapes similar to the vertebral bodies of the different species. Numerical results suggest that the external load is one of the main factors to determine the shape of vertebral bodies of teleost fish. Also, this mathematical model enables us to discuss what external load is important to form each vertebral shape of the different species.</p>