This study investigates an application of the wavelet transform to identify the characteristics of a nonlinear system of an elastically supported cylinder in cross-flow under uniform airflow. The envelope of the time response and instantaneous frequency is extracted using the wavelet transform to identify the nonlinear characteristics of the system. Responses within the range of the lock-in and nonlinear jump phenomena were investigated. Flow-induced vibration in a cylinder supported by two beams shows that the wavelet transform can identify the lock-in phenomena in both forward-sweep and backwardssweep experiments. The study shown that the vibration phenomenon caused by a flow in a beam supported cylinder medium with forward-sweep and backwards-sweep does not affect the damping characteristic due to the stiffness. The result will be beneficial in controlling vibration effect.