We use normal-incidence and wide-angle seismic data recorded on the Faroe Islands to study the crustal structure along two profiles extending east from the islands, across the Faroe shelf and into the Faroe-Shetland Basin. We show that massive basaltic lava flows extend eastward away from the Faroe Islands, having flowed across an older Mesozoic and early Paleocene sedimentary basin, and feathering out near the centre of the Faroe-Shetland Basin. Sediments beneath the basalts reach a thickness of several kilometres in the basin, but do not extend with a resolvable thickness beneath the Faroe Islands. The crustal thickness decreases toward the centre of the Faroe-Shetland Basin, showing that the basement beneath the centre of the basin has been stretched and thinned by a factor of at least two. The Faroe Islands themselves lie on a continental fragment, which had a total thickness of about 10-15 km of igneous rock added as extrusive lavas at the top, and as high-velocity intrusives near the base of the crust at the time of continental break-up in the Paleocene.