Abstract: Taking a single degree-of-freedom structural system as an example, the mathematical model of real-time dynamic hybrid testing for soil-structure interaction analysis (SSI-RTDHT) is established, where shaking table response delay and delay compensation strategy are included. Then the stability of the time-delayed system is investigated using the root locus technique based on Padé decomposition approximating the delay term. Finally, some numerical experiments are performed to validate the obtained stability conditions. The results show that the performance of the inherent mode is changed and SSI-RTDHT becomes conditionally stable due to the delay; the stability is worsen with increasing of the delay and the natural frequency of upper structure, and it is improved with increasing of the characteristic frequency of the foundation; the influence of the damping ratio of the upper structure on the stability is relatively small. The results also show that third-order polynomial compensation will make the stability worse, but it can improve the performance of the inherent mode.