The Transantarctic Mountains are a non-compressional belt located on the boundary between cratonic East Antarctica and non-cratonic West Antarctica. Here we present a time-evolving model for mountain uplift, formation of a small crustal root, depression of the hinterland Wilkes Basin, and formation of the West Antarctic Rift system (WAR). Using 2D thermo-mechanical models to study deformation of the tectonic boundary, we find that convergence of crustal material at the craton edge during extension results in formation of a small crustal root and surface uplift, consistent with observations. We suggest that the WAR formed adjacent to the craton, the weakest location in the region. The hinterland basin is a flexural depression; thermo-mechanical models yield no rifting in the hinterland as the craton is too strong. Our models indicate that uplift of the Transantarctic Mountains is related to formation of the WAR and flexural depression of the Wilkes Basin.