We present results from an active-source, onshore–offshore seismic reflection/refraction transect acquired as part of the PETROBAR project (Petroleum-related studies of the Barents Sea region). The 700 km-long profile is oriented NW–SE, coincident with previously published multichannel seismic reflection profiles. We utilize layer-based raytracing in a Markov Chain Monte Carlo (MCMC) inversion to determine a probabilistic velocity model constraining the sedimentary rocks, crystalline crust, and uppermost mantle in a complex tectonic regime. The profile images a wide range of crustal types and ages, from Proterozoic craton to Paleozoic to early Cenozoic rift basins; and volcanics related to Eocene continental breakup with Greenland. Our analyses indicate a complex architecture of the crystalline crust along the profile, with crystalline crustal thicknesses ranging from 43 km beneath the Varanger Peninsula to 12 km beneath the Bjørnøya Basin. Assuming an original, post-Caledonide crustal thickness of 35 km in the offshore area, we calculate the cumulative thinning (β) factors along the entire profile. The average β factor along the profile is 1.7 ± 0.1, suggesting 211–243 km of extension, consistent with the amount of overlap derived from published plate reconstructions. Local β factors approach 3, where Bjørnøya Basin reaches a depth of more than 13 km. Volcanics, carbonates, salt, diagenesis and metamorphism make deep sedimentary basin fill difficult to distinguish from original, pre-rift crystalline crust, and thus actual stretching may in places exceed our estimates.