The shape and thickness qualities of strip are influenced by the vibration of rolling mill.At present,the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of single stand mill,the study on the vibration of tandem rolling mill is rare.For the vibration of tandem rolling mill,the key problem is the vibration of the moving strip between stands.In this paper,considering the dynamic of moving strip and rolling theory,the vertical vibration of moving strip in the rolling process was proposed.Take the moving strip between the two mills of tandem rolling mill in the rolling process as subject investigated,according to the theory of moving beam,the vertical vibration model of moving strip in the rolling process was established.The partial differential equation was discretized by Galerkin truncation method.The natural frequency and stability of the moving strip were investigated and the numerical simulation in time domain was made.Simulation results show that,the natural frequency was strongly influenced by the rolling velocity and tension.With increasing of the rolling velocity,the first three natural frequencies decrease,the fourth natural frequency increases;with increasing of the unit tension,when the rolling velocity is high and low,respectively,the low order dimensionless natural frequency gradually decreases and increases,respectively.According to the stability of moving strip,the critical speed was determined,and the matching relationship of the tension and rolling velocity was also determined.This model can be used to study the stability of moving strip,improve the quality of strip and develop new rolling technology from the aspect of dynamics. The shape and thickness qualities of strip are influenced by the vibration of rolling mill. At present, the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of single stand mill, the study on the vibration of tandem rolling mill is rare.For the vibration of tandem rolling mill, the key problem is the vibration of the moving strip between stands.In this paper, considering the dynamic of moving strip and rolling theory, the vertical vibration of moving strip in the rolling process was proposed. Take the moving strip between the two mills of tandem rolling mill in the rolling process as subject investigated, according to the theory of moving beam, the vertical vibration model of moving strip was the rolling process was established. The partial differential equation was discretized by Galerkin truncation method. The natural frequency and stability of the moving strip were investigated and the numerical simulation in time domain was made. Simulation esults show that, the natural frequency was strongly influenced by the rolling velocity and tension. With increasing of the rolling velocity, the first three natural frequencies decrease, the fourth natural frequency increases; with increasing of the unit tension, when the rolling velocity is high and low, respectively, the low order dimensionless natural frequency gradually decreases and increases, respectively. According to the stability of moving strip, the critical speed was determined, and the matching relationship of the tension and rolling velocity was also determined. This model can be used to study the stability of moving strip, improve the quality of strip and develop new rolling technology from the aspect of dynamics.