One key evolutionary innovation that separates vertebrates from invertebrates is the notochord, a central element that provides the stiffness needed for powerful movements. Later, the notochord was further stiffened by the vertebrae, cartilaginous and bony elements, surrounding the notochord. The ancestral notochord is retained in modern vertebrates as intervertebral material, but we know little about its mechanical interactions with surrounding vertebrae. In this study, the internal shape of the vertebrae—where this material is found—was quantified in sixteen species of fishes with various body shapes, swimming modes, and habitats. We used micro-computed tomography to measure the internal shape. We then created and mechanically tested physical models of intervertebral joints. We also mechanically tested actual vertebrae of five species. Material testing shows that internal morphology of the centrum significantly affects bending and torsional stiffness. Finally, we performed swimming trials to gather kinematic data. Combining these data, we created a model that uses internal vertebral morphology to make predictions about swimming kinematics and mechanics. We used linear discriminant analysis (LDA) to assess the relationship between vertebral shape and our categorical traits. The analysis revealed that internal vertebral morphology is sufficient to predict habitat, body shape, and swimming mode in our fishes. This model can also be used to make predictions about swimming in fishes not easily studied in the lab, such as deep sea and extinct species, allowing the development of hypotheses about their natural behavior.