The biological world is full of systems whose component parts interact in a coupled non—linear fashion. As a result, studying any component of the system in isolation may not be representative of its natural behavior due to the coupling, and predicting the behavior of the entire system as a function of variation in any one parameter may be quite difficult due to the non—linear nature of the interactions. Swimming with whole body undulations is just such a system. The component parts of the swimming-system (muscle, skeleton, soft—tissue, and the surrounding fluid), are mechanically and physiologically coupled in a strongly nonlinear manner. Therefore, to predict the outcome of the entire system, i.e., swimming behavior, or to understand the role any one component plays as a determinant of the outcome, a mechanistic approach encompassing the form of the component's interactions is required. This approach is essential for developing scaling arguments, or discussing the consequences of morphological and physiological variation on behavioral and evolutionary “performance.” Below I outline an example of this method: a simplistic model of the mechanical interactions between the swimming system components of a leech. The model is based on in vitro characterizations of these components and first principle descriptions of their interactions. Solving the model's governing equations generates swimming behavior in the model organism. In addition, the model can predict the behavior of the swimming-system's component parts, allowing calculations of swimming performance and parameter variation not possible with other approaches.