This paper presents a dynamic model for a class of robotic fish propelled by a tail with a flexible fin. The robot is comprised of a rigid frontal link acting as a body and a rear link serving as the tail. The tail includes a rigid component, hinged to the body through a servomotor, which is connected to a compliant caudal fin whose underwater vibration induces the propulsion. The robot's body dynamics is modeled using Kirchhoff 's equations of motion of bodies in quiescent fluids, while its tail motion is described with Euler-Bernoulli beam theory, accounting for the effect of the encompassing fluid through the Morison equation. Simulation data of the model is compared with experimental data. Applications of the model include simulation, prediction, design optimization, and control.