Abstract: In order to reveal the self-excited frictional vibration law with high frequency and micro-amplitude of the sliding frictional interface in dry gas seals, the end face morphology of dry gas seals was characterized by fractal parameters. According to the re-established contact deformation model of the micro-convex body and the researches about the incipient sliding problem of the non-conforming elastic bodies under tangential force, the fractal model for tangential contact stiffness of dry gas seals was established. The key factors influencing the tangential contact stiffness were analyzed numerically, and the results showed that the tangential contact stiffness increased with the increased of fractal dimension, real contact area, and material properties factor. It decreased with the increased of the characteristic scale and friction coefficient. The effect of the coefficient of friction on the tangential contact stiffness was relatively small compared to the fractal dimension, the characteristic scale and the material properties factor. These researches provided a foundation for further study of the self-excited frictional vibration with high frequency and micro-amplitude in dry gas seals.