<p>Vortex induced vibration (VIV) of long span bridge is becoming an urgent problem in modern society. Because of the dense modal distribution in frequency domain, VIV of different modes can be excited in sequence within a narrow range of wind speed, which is well known as multi-mode VIV. However, such the multi-mode VIV phenomenon has not been well addressed theoretically. In this study, experimental and mathematical simulation is conducted for understanding and modelling multi-mode VIV, using a multi-span elastically supported beam. One of the interesting feature of multi-mode VIV observed in experiment is that, VIV of different modes are mutually exclusive, even though the lock-in ranges can be overlapped. The dual-oscillator model is firstly applied for the mathematical VIV simulation of a single mode. Then it is further extended to explore the multi-mode VIV of long span bridge by embedding the model into the governing function of a long span bridge. The proposed model shows good feasibility in simulating both the single- and multi-mode VIV, as the model can capture the most critical feature observed from the experiment. By examining the governing function of mathematic model, it is found that the Van Der Pol type nonlinear damping is responsible for the mutual exclusive feature between VIV of neighboring modes. The incremental harmonic balance method is adopted for detailed investigation of the multi-DoF nonlinear dynamic system. Two solution branches are identified, providing more comprehensive understanding of the multi-mode VIV characteristics of long span bridge.</p>