Flexible continuum robots exhibit a strong potential for approaching narrow and intricate spaces. However, such long flexible bodies often experience oscillations, making them unstable. To enhance their performance in order to realize rapid and precise movements, unnecessary vibrations should be suppressed. The authors have proposed a new type of continuum robot, aimed for firefighting; this robot, Dragon Firefighter (DFF), can fly using water jets. The DFF suffers from the same problem of body oscillation. In particular, a more challenging issue for the DFF is the use of limited number of actuators owing to the constraints of weight and water flow. Discrete locations of the actuators on the long body of a robot can generate uncontrollable resonant modes. This letter proposes a mechanical approach to suppress the oscillation passively without actuation control. The proposed mechanism is composed of wires threaded along the body and connected to rotary dampers to restrict the deformation of the body. First, a numerical model to simulate the oscillation and damping behavior was reported. A basic experiment with a 1-m-long flexible tube shows that the damping mechanism suppresses the vibration appropriately, which also corresponds well with the simulation. Second, a stability analysis of the simulation of the flying motion shows that the passive damping mechanism can improve the stability, with the convergence time becoming approximately 2.4 times shorter than that in the case without the mechanism. Finally, we apply the damping mechanism to a 3.6-m-long flying robot. The demonstration shows that the robot can float stably and that the damping mechanism works correctly.