Abstract We perform an integrated analysis of magnetic anomalies, multichannel seismic and wide-angle seismic data across an Early Cretaceous continental large igneous province in the northern Barents Sea region. Our data show that the high-frequency and high-amplitude magnetic anomalies in this region are spatially correlated with dykes and sills observed onshore. The dykes are grouped into two conjugate swarms striking oblique to the northern Barents Sea passive margin in the regions of eastern Svalbard and Franz Josef Land, respectively. The multichannel seismic data east of Svalbard and south of Franz Josef Land indicate the presence of sills at different stratigraphic levels. The most abundant population of sills is observed in the Triassic successions of the East Barents Sea Basin. We observe near-vertical seismic column-like anomalies that cut across the entire sedimentary cover. We interpret these structures as magmatic feeder channels or dykes. In addition, the compressional seismic velocity model locally indicates near-vertical, positive finger-shaped velocity anomalies (10–15 km wide) that extend to mid-crustal depths (15–20 km) and possibly deeper. The crustal structure does not include magmatic underplating and shows no regional crustal thinning, suggesting a localized (dyking, channelized flow) rather than a pervasive mode of magma emplacement. We suggest that most of the crustal extension was taken up by brittle–plastic dilatation in shear bands. We interpret the geometry of dykes in the horizontal plane in terms of the palaeo-stress regime using a model of a thick elastoplastic plate containing a circular hole (at the plume location) and subject to combined pure shear and pressure loads. The geometry of dykes in the northern Barents Sea and Arctic Canada can be predicted by the pattern of dilatant plastic shear bands obtained in our numerical experiments assuming boundary conditions consistent with a combination of extension in the Amerasia Basin sub-parallel to the northern Barents Sea margin and a mild compression nearly orthogonal to the margin. The approach has implications for palaeo-stress analysis using the geometry of dyke swarms. Supplementary material: Details on traveltime tomography model: Resolution tests, traveltime information and ray coverage are available at https://doi.org/10.6084/m9.figshare.c.3783542