A simplified linearized dynamic equation for the propulsion force generation of an Ostraciiform fish robot with elastically jointed double caudal fins is derived in this paper. The caudal fin is divided into two segments and connected using an elastic joint. The second part of the caudal fin is actuated passively via the elastic joint connection by the actuation of the first part of it. It is demonstrated that the derived equation can be utilized for the design of effective caudal fins because the equation is given as an explicit form with several physical parameters. A simple Ostraciiform fish robot was designed and fabricated using a microprocessor, a servo motor, and acrylic plastics. Through the experiment with the fish robot, it is demonstrated that the propulsion force generated in the experiment matches well with the proposed equation, and the propulsion speed can be greatly improved using the elastically jointed double fins, improving the average speed more than 80%. Through numerical simulation and frequency domain analysis of the derived dynamic equations, it is concluded that the main reason of the performance improvement is resonance between two parts of the caudal fins.