The continuous convergence between the Indian and Eurasian plates caused massive lithospheric deformation in the Tibetan Plateau and led to excessive crustal material escaping through its southeastern margin. However, the mechanisms that accommodate the escaping materials and whether they intrude into the Indochina Peninsula are continually under debate. Seismic Lg waves mostly propagate within the crust waveguide with an amplitude decay that is sensitive to crustal material properties, such as temperature, partial melting, and fracture. Therefore, Lg attenuation can be a useful indicator of potential crustal material escape. In this study, we developed a high‐resolution broadband Lg attenuation model in this region between 0.05 and 10.0 Hz, with the resolution reaching 1° in regions with dense raypath coverage. Prominent low‐Q anomalies beneath the southeastern margin of the Tibetan Plateau, correlating with previously observed low velocity, high conductivity and high Poisson’s ratio, may indicate possible high temperature and/or partial melting within a relatively weak crust, and suggest a north‐south interconnected corridor for gravity‐driven material flow. Through our results and other geological and geophysical observations, a dynamic model is suggested here by combining shallow rigid block extrusion and deep viscous crustal flow to explain crustal material escape in the southeastern margin of the Tibetan Plateau. Additionally, neither shallow extrusion nor deep material flow enter the Indochina Peninsula based on the relatively high Q values, which indicate a stronger crust there.