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In this paper a physics-based model is proposed for a biomimetic robotic fish propelled by an ionic polymer-metal composite (IPMC) actuator. Inspired by biological fins, a passive plastic foil is attached to the IPMC beam. The model incorporates both IPMC actuation dynamics and the hydrodynamics, and captures the interactions between the IPMC actuator and the plastic foil. Experimental results have shown that the proposed model is able to predict the steady-state cruising speed of the robotic fish under a periodic actuation input. Since the majority of the model parameters are expressed in terms of fundamental physical properties and geometric dimensions, the model is expected to be instrumental in optimal design of the robotic fish.