The eastern Tibetan Plateau (TP) is crucial to the exploration of plateau outgrowth mechanisms. Teleseismic attenuation may provide constraints on anelasticity in the lithosphere‐asthenosphere system and may therefore improve the understanding of plateau outgrowth and material extrusion. This study use dense array data across the eastern TP to measure relative attenuation from teleseismic P‐wave phases. These observations are then used to invert a 2D relative attenuation map and a 3D Qp−1 model. Weak attenuation is observed beneath the Sichuan Basin and most of the Dianzhong Block at depths of both 0–100 km and 100–200 km (Qp−1 < 0.003). Strong attenuation is observed beneath the eastern TP and southwestern Dianzhong Block at depths of 0–100 km (Qp−1 ∼ 0.01–0.13), but underneath the eastern TP only at depths of 100–200 km (Qp−1 ∼ 0.013–0.015). These results suggest a cratonic lithosphere underneath the Dianzhong Block similar to that beneath the Sichuan Basin. We assume that this is the cooled lithosphere remnant of the Permian Emeishan plume. In contrast, strong attenuation beneath the eastern TP would indicate a thick lower crust and asthenosphere with intense heating. The boundary between strong and weak attenuation lies close to the Longmenshan‐Xiaojinhe faults. We infer that the materials extruded eastward from the eastern TP cross this boundary into the southwestern Dianzhong Block in the lower crust, but stop at this boundary in the asthenosphere. Plain Language Summary: Seismic attenuation describes the energy consumption of seismic waves which reflects subsurface anelasticity and so can provide constraints on the ductile materials in the lower crust and the asthenosphere. Here we present a 2D relative attenuation map and a 3D upper mantle Qp−1 model for the eastern Tibetan Plateau. We find weak attenuation at depths above 200 km beneath the Sichuan Basin and most of the Dianzhong Block. Strong attenuation is observed beneath the southwestern Dianzhong Block at crustal depths, and underneath the eastern Tibetan Plateau at both crustal and asthenospheric depths. Our results suggest that the lithosphere beneath the Dianzhong Block has similar cratonic features to that beneath the Sichuan Basin. A thick and hot lower crust and asthenosphere with strong heat activity beneath the eastern Tibetan Plateau are also indicated by our attenuation images. Strong and weak attenuation are bordered by the Longmengshan‐Xiaojinhe faults. We would infer that the ductile materials extruded from the Tibetan Plateau cross this boundary into the southwestern Dianzhong Block in the lower crust, but not in the asthenosphere. Key Points: Weak attenuation observations beneath the Dianzhong Block suggest the lithosphere there has similar cratonic features to that beneath the Sichuan BasinA thick lower crust and asthenosphere with strong heat activity beneath the eastern Tibetan Plateau are inferred from strong‐attenuation observationsThe eastward extrusion of the Tibetan Plateau crosses the Xiaojinhe Fault into the southwestern Dianzhong Block in the lower crust, but not in the asthenosphere [ABSTRACT FROM AUTHOR]