Recent acceleration and thinning of Thwaites Glacier, West Antarctica, motivates investigation of the controls upon, and stability of, its present ice-flow pattern. Its eastern shear margin separates Thwaites Glacier from slower-flowing ice and the southern tributaries of Pine Island Glacier. Troughs in Thwaites Glacier’s bed topography bound nearly all of its tributaries, except along this eastern shear margin, which has no clear relationship with regional bed topography along most of its length. Here we use airborne ice-penetrating radar data from the Airborne Geophysical Survey of the Amundsen Sea Embayment, Antarctica (AGASEA) to investigate the nature of the bed across this margin. Radar data reveal slightly higher and rougher bed topography on the slower-flowing side of the margin, along with lower bed reflectivity. However, the change in bed reflectivity across the margin is partially explained by a change in bed roughness. From these observations, we infer that the position of the eastern shear margin is not strongly controlled by local bed topography or other bed properties. Given the potential for future increases in ice flux farther downstream, the eastern shear margin may be vulnerable to migration. However, there is no evidence that this margin is migrating presently, despite ongoing changes farther downstream.