The SMA vibration isolation system of double-flag ring is established, and the method of fast solving the SMA vibration isolation system of doubleflag ring is put forward by the average method and stability analysis. Four kinds of amplitudefrequency curves and their critical loads produced by different load amplitudes are obtained, the appropriate amplitude-frequency curve form for vibration isolation design is selected, and the vibration isolation effect is verified by the transmission rate curve. The results provide a reference for the design of vibration isolation. The relationship between the peak response and the load amplitude is solved, so that the amplitude-frequency curve form can be determined by the load size, and the peak response frequency can be determined to provide a reference for avoiding resonance. The influence of the parameters of the hysteresis curve on the amplitude-frequency curve is studied, and the recommended value range of the parameters of the hysteresis curve is given, which provides a reference for the design and manufacture of SMA.