Abstract: A new model of coupling structure and wake oscillator invortex-induced vibration (VIV) is established. It is based on forcebalance between structure and near wake flow. The nonlinear near wakevortex dynamics is modeled by a nonlinear oscillator satisfied the Van derpol equation. According to the study of 2-DVIV, the coupling model describes the featuresof response versus reduced velocity qualitatively and quantitatively. These results prove that the peak amplitude of structureA_\max ^\ast decreases as the mass-damping (m^\ast + C_A )\zeta increases. An empirical formula on A_\max ^\ast versus (m^\ast + C_A)\zeta is obtained based on these results. The present 3-D coupling modelis employed in the study of 3-D VIV of flexible slender cylinder. Dynamicresponse behavior of uniform flow presents a change from standing wave totraveling wave. Under non-uniform flow whose profile is sinusoidal, thestructure vibration is a combination of standing and traveling waves alongthe span. These results are similar with those from direct numericalsimulation (DNS), and some other previous results.