With the high G value of vibration, outstanding sieving behaviors of a flip-flow screen are more likely to appear, but structural damages are aggravated under the high amplitude vibration. Considering rubber springs role on the vibration energy dissipation, viscoelasticity of rubber springs (i.e., shear springs and vibration isolation springs), is noticed to deal with the above contradiction. However, when rubber springs experience large amplitude vibration, viscoelastic responses influence more on the amount of damping than in the linear (i.e., small amplitude) vibration regime, as the frequency dependence of rubber springs is noteworthy. For this purpose, the Generalized Maxwell model is used to depict the frequency dependence of rubber springs and the practical damping is converted to a series damping parameters of the system, numerical models of the flip-flow screen under startup and shutdown modes and steady working conditions are proposed and verified firstly. Secondly, in order to explore kinetics responses of the elastic screen panel under different rubber springs damping coefficients, nonlinear finite element model of which is established. Finally, effects of rubber springs nonlinear damping on screen frames vibrations and screen panels nonlinear responses are studied. Results indicate that hysteretic damping of rubber springs can effectively solve the conflict between vibration strength and structural reliability of the flip-flow screen, since the low sensitivities of maximum stresses and the high sensitivities of accelerations to rubber springs damping are found.