The suppression of mechanical resonance in dual-inertia servo systems remains an important research topic. First, a dual-inertia system composed of a driving motor, a transmission shaft, and a load motor is modeled. Relevant transfer functions are obtained through Laplace transform, and their resonance characteristics are analyzed. The relationships between the system’s natural resonance frequency, anti-resonance frequency, the elastic coefficient of the transmission shaft, and the rotational inertias of the motor and the load are clarified. Then, three resonance suppression methods, namely the notch filter, the pole placement method based on PI control, and active disturbance rejection control, are studied, and their principles and control strategies are expounded respectively. Simulation experiments are carried out using the Matlab/Simulink platform to compare the performances of different methods during the motor speed rising stage and when the load torque changes. The results show that the notch filter can effectively suppress resonance, the pole placement method can further reduce the speed difference between the motor and the load, and active disturbance rejection control performs best in suppressing resonance, controlling overshoot, and ensuring dynamic stability, with overall superior control performance.