During the preparation of the high-speed moving membrane, due to the parallelism error of adjacent support part such as guide roller, tension of the film is prone to uneven distribution along the width direction. This work aims to study approaches to improve the working stability of printing equipment. The transverse vibration differential equation was derived according to the D’Alembert principle and transformed into dimensionless form by introducing the dimensionless quantity. The calculation of complex frequency equation of an axially moving membrane was done by the analytical method. The curves of the dimensionless frequency with the dimensionless speed under different parameters were obtained. When the tension coefficient and tension ratio were increased or length width ratio was decreased, the critical dimensionless velocity of the membrane system was increased, and the system was more stable. In conclusion, the critical dimensionless velocity of the thin membrane system under different tension ratio, tension coefficient and length width ratio is obtained through the study.