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In this paper, we develop a modeling framework for studying free-locomotion of biomimetic underwater vehicles propelled by vibrating ionic polymer metal composites (IPMCs). The motion of the vehicle body is described using rigid body dynamics in fluid environments. Hydrodynamic effects, such as added mass and damping, are included in the model to enable a thorough description of the vehicle's surge, sway, and yaw motions. The time-varying actions exerted by the vibrating IPMC on the vehicle body, including thrust, lift, and moment, are estimated by combining force and vibration measurements with reduced order modeling based on modal analysis. The model predictions are validated through experimental results on a miniature remotely controlled fish-like robotic swimmer.