The mountain range at the steep eastern edge of the Tibetan Plateau, the Longmen Shan, was deformed by a Mw7.9 earthquake with oblique thrust and strike-slip motion in 2008. The tectonic processes and structure of the lithosphere beneath this range have been controversial. Gravity measurements reflect the distribution of mass within the Earth, including the large load of rock above the geoid in mountain ranges. We investigate the response of the lithosphere to the load of the Longmen Shan and estimate the flexural rigidity or effective elastic thicknessTeusing new gravity data acquired by recent satellites and the combined GOCO2S and EIGEN-6c datasets. The free-air gravity anomalies over the Longmen Shan show that its mass is supported by flexure of the adjacent Sichuan Basin lithosphere, similar to the flexural support of the Himalayas. Analysis of a stacked profile of the free-air anomalies shows that the effective elastic thickness of the basin lithosphere is greater than 10 km, but has a broad minimum misfit function with no upper limit on the thickness. Two-dimensional admittance analysis shows theTe of easternmost Tibet is very low, approximately 7 km.