Animal locomotion is generally a very complicated phenomenon involving an interaction between neural spike trains activating muscles, which causes motion, which in turn creates feedback from the environment that affects all elements in the process. In this talk I will describe a model for one of the simplest vertebrates, the lamprey. We connect a simple model for muscle forces stimulated by electrical activity to an elastic rod. A wave of electrical activity traveling the length of the rod creates a corresponding wave of curvature which develops a thrust from the surrounding fluid that pushes the animal forward. I will explain the various aspects of this model and how they are coupled together. We will see how some phenomena can be explained with this model, including an observation made a few decades ago that in real animals the wave of electrical activity travels faster than the corresponding wave of curvature.