In this study, we investigate the thermo-mechanical controls on the formation of the Ross Sea basin (Antarctica) and the uplift of the adjacent Transantarctic Mountains (TAM) rift shoulder, which started in the Late Cretaceous and continued until the present time. Quantitative forward modelling has been performed along three 700 to 800 km long East-West offshore profiles, extended inland to the front of the TAM. The modelling is constrained by an extensive database of multichannel seismic (MCS), refraction seismic, Ocean Bottom Seismographs (OBS), and gravity data. MCS data is tied to well stratigraphy from DSDP leg 28, CIROS-1 and MSTSS-1. Quantitative estimates of uplift of the TAM are provided by previous work on apatite fission track analysis. We incorporate the finite strength of the lithosphere in basin formation models using the concept of the level of necking. Lateral variations of necking level and associated bulk theological properties (with necking levels ranging from 15 km in the northernmost, to 20 km in the central and 23 km to the southernmost profiles) are required to explain the observed crustal geometries. High values of effective elastic thickness (more than 30 km) and pre-rift lithospheric thicknesses (220-230 km), indicating a cold lithosphere in a pre-rift cratonic setting, are consistent with elevation of the rift shoulder. The western parts of the profiles appear to have unusually high stretching values without the development of oceanic crust. Inferred average values of stretching factors vary from 2.3 to 2.8, equivalent with extension in the Ross Sea of 115% to 140%. The modelling result for the uplift of the TAM predicts a late Cretaceous tectonic uplift of about 1.5 to 2.0 km, and a Cenozoic uplift of about 1.3 km restricted to southern Victoria Land. (C) 1999 Elsevier Science B.V.