This paper considers fish-like designs of underwater vehicles with oscillating tails and fins. On the base of dynamic analysis of a robotic fish motion, two original methods to produce driving force have been recently patented. The first method is based on the cyclic variation of the effective working area of the fin during the operation of a propulsive device. The optimal control law for variation of an additional area of a vibrating fin has been found. It is shown that the realization of this law ensures maximal positive impulse of driving forces and minimizes energy losses. New designs of one-tail and two-tail propulsive devices with varying working area of vibrating fin have been patented. In accordance with another developed method, driving force is produced by an internal two-stage gyroscopic device. In this case, vibrations of the tail of the fish are generated due to the action on it of reaction torque from a swinging internal high speed rotor with two degrees of freedom. The proposed device has no external moving parts; therefore, its operation in various surroundings becomes more reliable and effective. The results of theoretical study are confirmed by experiments with robot fish models.