<p>Inspired by the crucial role of the tail in crocodile locomotion, we propose a novel rigid-flexible coupled tail structure design. The tail design reduces the number of required actuators, enables undulatory propulsion in swimming, and provides additional support during terrestrial crawling. However, when the tail lifts off the ground during land crawling, its flexible underactuated structure tends to oscillate randomly due to minimal damping. These oscillations impart disruptive reaction torques to the body, critically impairing locomotion stability. To tackle this issue, we employed the standard Denavit-Hartenberg (DH) method and Newton-Euler equations to formulate a rigid-flexible coupled dynamic model for the tail, in which distributed elastic forces are embedded as internal forces in the force balance equations. Based on this model, we propose an oscillation suppression strategy based on an energy-optimized Nonlinear Model Predictive Controller (NMPC) with a single joint torque as the control input. This controller solves a constrained multi-objective optimization problem to effectively suppress the underactuated oscillations of the tail. Finally, experimental comparisons validate the accuracy of the dynamic model, and simulations based on this model substantiate the effectiveness of the oscillation suppression strategy.</p>