Strip steel vibrations is inevitable in the rolling process of tandem mill, and the coupled model between elastoplastic body of strip steel and main drive system directly affects the overall dynamic performance of rolling mill. According to the movement mechanism of strip steel and main drive system, the main drive system was simplified to a two-degree-of-freedom discrete model and the strip steel was simplified to an axially moving Euler beam, the coupled vibration mechanical model of transverse and longitudinal vibrations of strip steel and torsional vibration of main drive system was established. Then, the nonlinear vibration differential equations of the coupled model were derived with Hamilton’s principle. The modified iteration method and the Kantorovich averaging method were used to solve the differential equations. Finally, by using the Matlab simulation, the influence of torsional vibration fundamental frequency of main drive system on strip steel vibration characteristics was discussed. The results can enrich the theoretical achievements on vibration of rolling mill, and it is valuable for transforming theoretical results into engineering applications.