This study aims to optimize the design of precision coating presses and study the transport stability of membrane during precision coating. The air resistance was modeled as a follower force. The influences of the follower force, the tension ratio and the aspect ratio on the membrane stability were analyzed by the differential quadrature method. Through programming and calculation, it was found that the unstable region of the edge-supporting edge was larger than that of the four-sided fixed edge under the same conditions, and the stable region of the system decreased with the increase of the tension ratio. The results show that under the same follower force, the tension ratio has a significant effect on the stability of the membrane vibration. This study provides theoretical guidance and basis for the optimal design and manufacture of precision coating presses and the transmission stability of membrane during precision coating.