The beaver-like underwater robot can crawl and swim, playing a significant role in the exploration of amphibious environments. Its fan-shaped tail can provide part of the forward power and maintain its motion stability. However, no mature dynamic modeling method is available to model its tail motion until now. This paper presents a segmented dynamic modeling approach to build the propulsion and lift models of a beaver-like robot tail. It combines hydrodynamics and material mechanics and forms the fan-shaped flexible dynamics modeling theory. A performance index is created to measure the motion performance of the tail, which provides a theoretical basis for describing and evaluating the tail function. Simulations and experiments are conducted to verify the tail dynamic model and the motion performance under different swing amplitude coefficients. The obtained optimal swing amplitude coefficient is 2, which lays the foundation for robot motion control. The study could further promote the development of dynamic modeling and analysis for other underwater biomimetic robots.