For the synchronous drum type permanent magnet coupling, the torque curve between the active permanent magnet rotor and the driven permanent magnet rotor is calculated by simulation software. The equivalent torsional rigidity K of permanent magnet coupling is defined by linearization near the working points of the torque curve. Using reasonable assumption and simplification, the dynamic differential equation of synchronous permanent magnet coupling is established in the course of work, and the system transfer function is obtained by Laplace transform. When working, the permanent magnet coupling will often encounter the impact load or the sine wave load. The system is simulated under the unit pulse excitation and the harmonic excitation respectively in order to solve the time response curve. It is crucial to verify the shock resistance and vibration reduction behavior of synchronous permanent magnet coupling. Our study shows that when permanent magnet coupling encounters the impact load in the course of work, the angle difference increment θ(t) will continue to oscillate and decay until elimination with the natural frequency of system. When permanent magnet coupling encounters the harmonic load, the transient state response of angle difference increment θ(t) will continue to oscillate and decay until elimination with the natural frequency of the system. The steady state response shows that the angle difference increment θ(t) persists with the excitation source. The frequency of steady state response is the same as the frequency of forced vibration，but the phase angle lag behind the excitation source. The amplitude of the steady state response is related to the torsional rigidity of permanent magnet coupling. Finally, it is proved that permanent magnet coupling has excellent properties of shock resistance and vibration reduction.