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This paper presents the steps for the mathematical modelling of a fish robot with four degrees of freedom (DOF) called UC-Ika 1. The swimming motion of the robot, which is inspired by tuna fish, needs to generate an undulatory motion by its tail peduncle and caudal fin. Hence, the robot has the benefit of a tail mechanism that plays a determining role in the dynamic behaviour of the robot. Analysing this tail mechanism and the hydrodynamic forces acting upon the fish robot, the governing equations of motion of the robot are derived. Solving these dynamic equations reveals that the robot has a cruising speed of 0.29 m/s, a slight oscillation in the Y direction, and a small swing around its centre of mass. These results are validated by the experimental results of UC-Ika 1.