The work aims to analyze the mechanical vibration generated when the spiral corrugated flying shear machine is cutting corrugated board and to reach the cutting precision necessary for production by reducing the vibration response of upper and lower cutter shafts. The dynamics model of spiral corrugated flying shear machine was established. Vibration analysis was carried out by means of mathematical analysis and Ansys simulation software. By comparing the analytical results with the Ansys simulation results, they proved that the vibration model established was correct. Based on the analysis of vibration characteristic parameters of flying shear machine, the method used to reduce the vibration response was proposed, namely carbon fiber material was used to control the vibration response of upper and lower cutter shafts within 0.07 mm, so as to reach the cutting precision requirements of flying shear machine. All the above have proved that it is effective to study the vibration characteristics, reduce vibration response and improve cutting quality with the dynamic mathematical model and Ansys simulation.