As regulations concerning ship vibration and noise are becoming stricter, considerable attention is being drawn to prediction technologies for ship vibration and noise. In particular, the resonance and lock-in phenomena caused by vortex-induced vibration (VIV) have become considerably important with increases in the speed and the size of ships and ocean structures, which are known to cause structural problems. This study extends the fluid-structure interaction (FSI) analysis method to predict resonances and lock-in phenomena of high modes and VIV of ship rudders. Numerical stability is secured in underwater conditions by implementing added mass, added damping, and added stiffness by applying the potential theory to structural analysis. An expanded governing equation is developed by implementing displacements and twist angles of high modes. The lock-in velocity range and resonant frequencies of ship rudders obtained using the developed FSI method agree well with the experimental results and the analytic solution. A comparison with local vibration guidelines published by Lloyd’s Register shows that predictions of resonances and lock-in phenomena of high modes are necessary in the shipbuilding industry due to the possible risks like fatigue failure.