The Transantarctic Mountains, which mark the boundary between East and West Antarctica, arguably form the largest continental rift-shoulder structure on earth. Viscoelastic finite element analysis has been used to model the present state of uplift, and of subsidence of the adjacent Victoria Land Basin, as the response to the lithospheric tension and basal upthrust produced by the low density uppermost mantle underlying adjacent West Antarctica and extending for 50–70 km beneath the Transantarctic Mountains. The observed uplift and complementary subsidence across the Transantarctic Fault can be matched by Model TAM4 with a low density upper mantle (−50 kg/m 3) extending 70 km westwards from the fault and from 45 to 200 km depth. The East Antarctic lithosphère as modelled has an elastic thickness of 100 km which decreases to about 25 km at the eastern margin of the craton where the uplift is occurring and is 25 km thick beneath adjacent West Antarctica. Alternatively, in Model TAM5 low density upper mantle extends for only 50 km beneath the Mountains, and an upper mantle of smaller density contrast (−36 kg/m 3) extending proportionately deeper to 254 km depth is required to match the observations. A horizontal deviatoric tension of 120 MPa (TAM4) or 150 MPa (TAM5) occurs in the thin elastic lithosphere of West Antarctica as a result of the sub-lithospheric loading caused by the low density upper mantle, but this dies off into East Antarctica on passing through the Mountains. Additionally, there are substantial superimposed bending stresses due to flexure on both sides of the fault. Such high stresses suggest elastic failure to be occurring, which underscores the paradox of the apparent aseismicity of Antarctica. The result of superimposing a supplementary compression averaging 20 MPa across the edge of the 100 km thick lithosphere of East Antarctica is to reduce the amplitude of the flexural uplift by about 19% and the subsidence by about 32% as a result of the reduced deviatoric tensions. A superimposed lithospheric tension has the exact opposite effect. The models with superimposed stresses suggest that the main plate interior stress field is less important than the locally derived loading stresses in the present support of the Transantarctic Mountains.