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Soft actuation materials, such as ionic polymer-metal composites (IPMCs), are gaining increasing interest in robotic applications since they lead to compact and biomimetic designs. In this paper, we propose the use of soft actuation materials as active joints for propelling biomimetic robotic fish. An analytical model is developed to compute the thrust force generated by a two-link tail and the resulting moments in the active joints. The computed joint moments can be combined with internal dynamics of actuation materials to provide realistic kinematic constraints for the joints. Computational fluid dynamics (CFD) modeling is also adopted to examine the flow field, the produced thrust, and the bending moments in joints for the two-link tail. Good agreement is achieved between the analytical modeling and the CFD modeling, which points to a promising two-tier framework for the understanding and optimization of robotic fish with a multi-link tail. We also show that, comparing to a one-link bending tail, a two-link tail is able to produce much higher thrust and more versatile maneuvers, such as backward swimming.