To study the flow-induced small-amplitude vibration of Tainter gates with an eccentric trunnion and small gate openings, which will be influenced significantly by the reservoir depth, this study presents an analytical method to derive the hydraulic pressure induced by an arbitray motion of the gate. In the analysis, Rayleigh's potential theory developed for dissipative-wave radiation problems is applied to reduce the flow fluctuation phenomina to an initial-boundary value problem which can be solved by making use of mathematical techniques such as the Fourier series transform, Fourier integral transform and Laplace transform. Consequently, the equation of gate motion is derived in the form of a homogeneous differential-integral equation. The equation of gate motion is then reduced to a dimensionless form to reveal the major factors which describe the dynamic similarities between the flow induced vibration system.