When the critical wind speed for the vortex induced resonance is close to that for the  quasi steady galloping, a kind of coupled wind-induced vibration is easy to occur on a rectangular bar, which is different from the conventional vortex-induced vibration and divergent galloping.It is a kind of “soft galloping” phenomenon that the response amplitude increases linearly with the increase of wind speed.The mass and damping are the key parameters that affect the coupling degree and the amplitude response estimation.Based on a set of models with 1.2 width-height-ratio rectangular section member, by adjusting the equivalent stiffness, the equivalent mass and the damping of the model system, contrast experiments on the wind-induced vibration responses were carried out in the following cases: the same mass with different damping , the same damping with different mass and the same Scruton number with different mass and damping combination under the condition of uniform Reynolds number.The results show that in the coupling state, the influences of mass and damping parameters on the amplitude responses of “soft galloping” are independent and the weights are the same; for the “soft galloping” amplitude response, there is a Scruton number “locked interval (12.4-30.6)”.In the “locked interval”, the linear slope of the dimensionless wind speed amplitude response curve does not change with the Scruton number.Moreover, a “transition interval (26.8-30.6)” for the Scruton number coexists, where the coupled wind-induced vibration state is transferred to uncoupled state; the empirical formula for “soft galloping” response amplitude estimation is modified, which can be used to predict the amplitude within the designed wind speed range of similar engineering members.