A new 3D lithospheric model has been constructed using high-resolution gravity data from the Irish National Seabed Survey. The sedimentary component of the model incorporated density variations due to laterally varying overcompaction associated with Cenozoic denudation. After optimisation based on gravity inversion, regional crustal thickness variations were defined which are in reasonable agreement with the results of wide-angle seismic experiments. High crustal extension factors (β>5) characterise the deeper parts of the Rockall and Porcupine basins and in places the model indicates extreme stretching (β>10) beneath these basins. This could be because of instability in the gravity inversion, although other recent investigations have independently suggested similarly high extension factors. In contrast, the Hatton Basin is characterised by an apparent extension factor of about 2. The modelling resolves a pattern of NE-to NNE-trending local Mesozoic basins on the margins of the Rockall Trough, helping to delineate structures that were previously only sparsely sampled by seismic surveys. It appears possible that rifts with similar trends underlie the volcanic rocks which obscure the deeper parts of the Hatton Basin. The linear trends of the basins to the south and east of Ireland are interpreted to have been inherited from a basement fabric that was initially established during the late Precambrian assembly of this basement and subsequently subjected to Caledonian and Variscan reactivation. Magnetic modelling indicates that the variations in the thickness of the crystalline crust predicted by the gravity models can explain the regional magnetic anomaly patterns over the Rockall and Porcupine basins, but that significant additional magnetic material (probably igneous rocks of both Palaeogene and Cretaceous ages) is required to explain the anomalies in the Hatton Basin region. The magnetic signature of the Rockall Basin is distinctly different to that over the basement (of similar apparent thickness) formed during mid Cretaceous (C34N) opening of the ocean basin to the south. This is an impediment to hypotheses that invoke mid Cretaceous sea-floor spreading rather than intracontinental rifting to explain the development of the basin. The exception is in the extreme south of the basin where the volcanism associated with the Barra Volcanic Ridges combined with indications of relatively strong lithosphere could be evidence of incipient ocean opening.