With the goal of robustly designing and fabricating a soft robot based on a caterpillar featuring shape memory alloy (SMA) actuators, analytical and numerical models for a soft robot were created based on the forward crawling motion of the Manduca sexta caterpillar. The analytical model features a rod theory and the mechanics of undulation were analyzed using a motion pattern based on the 'Witch of Agnesi' curve. Complementing these models, experiments on a SMA actuator sample were performed in order to determine its flexural rigidity and curvature as a function of the actuation voltage. A series of these actuators can be modeled as a system of rigid bodies connected by torsional springs. As these bodies are actuated according to the motion pattern based on the individual caterpillar segments, ground contact forces are calculated and analyzed to determine the requirements of successful forward locomotion. The energetics of the analytical and numerical models are then compared and discussed.