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In the process of guide roller transmission, the geometric nonlinearity caused by the lateral vibration of the flexible electronic membrane will result in the divergence and instability of the membrane velocity, thus affecting the printing accuracy. In this paper, in order to engineer the exact condition that affecting the printing accurancy, the Elliptic integral method, whose effectiveness has been verified for its soluted result, is consistent with the one concluded from L-P method and He's Frequency formula while soluting the nonlinear vibration equation, respectively, on basis of Von Karman’s large deflection theory and Hamilton’s principle, is mainly applied, and thus provide a theoretical support for the design and manufacture of high-precision flexible electronic printing press.