The Transantarctic Mountains form one of the largest rift shoulder uplifts in the world. Uplift of the mountains, and coeval subsidence in the Ross Embayment, are modelled with both elastic flexure equations and with the viscoelastic finite element method. Most of the geological constraints are adequately satisfied by the elastic flexure equations. Uplife of the Transantarctic Mountains requires an uplift force/unit area of about 200 MPa over an approximate 60 km zone at the edge of the East Antarctic plate. This uplift is attributed to a sum of the following three processes: thermal conduction of heat from the rifted west Antarctic lithosphere into the older, cratonic lithosphere of East Antarctica; an isostatic uplift linked to a normal fault that penetrates the whole lithosphere; and about 2 km of erosion that has occurred at the mountain front.