This book presents a novel method for the numerical simulation of swimming animals. It includes a review of the hydrodynamics of swimming, a description of the CFD model adopted, and a description of the results obtained by applying this model to the cownose ray. This method is developed for the open-source software OpenFOAM and relies on an overset mesh. A custom library is added to the solver to include the equations of the kinematics of the animal under investigation, combining the deformation of the fish fins with the computed displacement and rotation of the animals body. The presented method helps investigate the dynamics of any animal moving in a fluid, provided that its kinematics is known, and in this work, it is applied to investigate the hydrodynamics of a cownose ray. This book is intended for researchers and engineers who aim to deeply understand the hydrodynamics of fish swimming and to design bioinspired autonomous underwater vehicles or novel propulsion systems.