Abstract: A two-parameter lift-oscillator model is adopted to describe vortex shedding excitation on tall cylindrical structures. A theoretical model of a cylindrical structure with multi-degree-of-freedom is first formulated and the governing partial differential equations are solved using the finite difference approximation. Numerical analysis of vortex-induced vibration responses of cylinder structure is performed using the time-matching approach. The obtained results indicate that the present two-parameter lift-oscillator model can predict classical lock-in phenomena and the amplitude peak effect of cylindrical structures in gradient wind field. The influences of structural damping and model parameters on the vortex-induced vibration responses and critical wind speed of chimneys are discussed in detail.