We present tectonic models of progressive basin formation in the south-west Barents Sea derived as part of the PETROBAR project (Petroleum-related studies of the Barents Sea region). The basin architecture developed as a multi-stage rift preceding the creation of the sheared/transtensional margin conjugate to NE Greenland. N- to NNE-striking basins, with sediment thicknesses in places exceeding 15 km, are separated by basement highs. We use two basin analysis approaches, BMT™ backstripping and TecMod™time-forward modelling, to determine stretching factors through time along the profile PETROBAR-07. This 550 km-long profile derived from wide-angle reflection/refraction seismic data acquired in 2007, coincident with deep multichannel seismic reflection data. Detailed stratigraphic analysis of the reflection profile, in concert with a dense grid of 2D profiles tied to wells, provides timing and water depth constraint for the models. Velocity analysis of the wide-angle data provides constraint on the cumulative crustal stretching. The north-west trending cross-section extends from continental craton, at the Varanger Peninsula, to within 16 km of the interpreted continent–ocean boundary. Rifting along the profile was episodic, with four distinct phases of basin formation during the Carboniferous, the Late Permian–Triassic, the Late Jurassic–Early Cretaceous and the Late Cretaceous–Eocene. Collectively, the basins exhibit a general trend of younging, narrowing, and deepening oceanward, suggesting a gradual focusing of rifting prior to final breakup. Cumulative stretching factors derived from BMT and TecMod correlate well with observed crustal thinning, and the two models provide uncertainty bounds for stretching factors for the separate rift phases. In contrast to orthogonally rifted margins, stretching is relatively minor immediately prior to transform breakup, with greater stretching occurring during earlier rift phases.