This study systematically investigates the impact of pre-stretching amount (PSA) on the acceleration, motion status, and screening efficiency of the Flip-flow screen plate (FFSP). Initially, a nonlinear spring-multi-body model of the FFSP is established. Subsequently, the acceleration signals at the midpoint of the FFSP under various PSAs are measured and analyzed. The nonlinear stiffness coefficient of FFSP along the vertical direction is then determined and it is found that simplifying the nonlinear spring-multi-body system to a nonlinear spring-tri-body system under the experimental conditions can maintain the calculation error of FFSP’s acceleration within 30%. Phase and Poincaré mapping diagrams of the FFSP under different PSAs are subsequently created to illustrate the impact of PSA on the motion status of the FFSP. Finally, screening experiments are performed to study the optimal PSA for a kind of bituminous coal from Shanxi province.