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Vulnerable transmission lines or sections have great impacts on large-scale blackouts and cascading failures in power grids. A comprehensive scheme to study transmission vulnerability based on the fault chain theory of security science is proposed in this paper. In this scheme, the cascading failure process and its generic features are described according to a fault chain. Power flow transfer, sequent overload of lines, and damage of transmission sections are modeled and normalized to predict all the fault chains. On the basis of the fault chains, a new vulnerability assessment index is presented to identify critical lines and sections contributing to failure extension and system instability. The effectiveness of the proposed assessment scheme is demonstrated via numerical examples on three power systems. Considering operation properties and transient impact, the proposed scheme can be executed in an efficient way.