Understanding the vibrational characteristics of power transformers is significantly important in their design and monitoring. In this contribution, a model with a multi-physics coupling simulation of the electrical circuit, magnetic field, and solid mechanics is developed to investigate the characteristics of the transformer vibration. After describing the model, the harmonic contents of the vibration signals and their variation in the case of mechanical faults are studied. It is shown that under normal operating conditions, the fundamental vibration frequency of 100 Hz has the maximum amplitude, while in the case of mechanical faults, the amplitudes of 200 Hz and 300 Hz harmonics increase dramatically compared to the fundamental harmonic. The influence of vibration sensor position is investigated too, which indicates that the area near the tank bottom is the best position to gather vibration signals. Moreover, the mechanical resonance frequencies of the transformer, along with their mode shapes, are addressed in this paper. Finally, the influence of mechanical changes on the vibration energy distribution in the tank surface is explored. The results of the paper suggest possible diagnosis methods for condition monitoring of transformers, such as using the vibration energy distribution on the tank surface or analyzing the vibration harmonics.