The complex torque coefficient method and eigenvalue analysis are two main methods for analyzing the modal damping of subsynchronous resonance（SSR） in compensated transmission systems. However， both methods need complicated and detailed models of full system， and the conclusions can only be summarized from the large amount of calculating results without intuitionistic explanations. An explicit mathematical expression of multi-mode SSR torsional damping in an equivalent single-machine infinite-bus system is deduced and verified by comparing with the results of eigenvalue analysis. This obtained formulas are helpful to better understand the principle of SSR and the influence of different system parameters on SSR. Moreover， it also provides an efficient method to quickly assess the risk and severity of SSR in practical engineering applications.