The paper examines the dynamic features of traveling wave by numerical simulation, and the effect of hydrodynamic damping and initial tension on traveling wave were presented for the vortex?induced vibration(VIV) of a long slender cylinder. The simulation was carried out by using a modified wake oscillator model which considered the coupling of in?line (IL) and cross?flow (CF) motions for VIV. The variation of the tension along the length of the model and the wake diffusion were considered. A method that was used to assess the contribution of traveling waves in whole vibration waves was also introduced, where the traveling wave ellipse was employed to scale the ratio of travelling wave component to overall vibration wave. The simulation results show that the traveling wave ratio presents a roughly increasing tendency with the increase of velocity, but falls suddenly at a critical velocity where the mode number is changed. Meanwhile, it is found that the hydrodynamic damping influences the contribution of traveling waves greatly. The lager the fluid damping is, the greater the contribution of traveling wave in whole vibration wave is. For the case with a hydrodynamic damping of 1.1, the traveling wave ratio is greater than that for the cases with hydrodynamic damping of 0.9 and 0.7. The velocity where the traveling wave ratio suddenly falls is controlled by the initial tension, while the initial tension influenced the mode order.