In this paper, we develop a new dynamic model for a robotic fish propelled by a flexible tail actuated at the base. The tail is modeled by multiple rigid segments connected in series through rotational springs and dampers, and the hydrodynamic force on each segment is evaluated using Lighthill's large-amplitude elongated-body theory. For comparison, we also construct a model using linear beam theory to capture the beam dynamics. To assess the accuracy of the models, we conducted experiments with a free-swimming robotic fish. The results show that the two models have almost identical predictions when the tail undergoes small deformation, but only the proposed multisegment model matches the experimental measurement closely for all tail motions, demonstrating its promise in the optimization and control of tail-actuated robotic fish.