The stress distribution and plate boundary force produced by ridge push are modelled by elastic/viscoelastic finite element analysis in oceanic lithosphere and in an adjacent continent separated by a passive margin. Models are presented for both a normal slow-spreading ridge and for one underlain by an anomalously low density upper mantle associated with a hot spot which gives rise to 1 km extra elevation of the sea floor. The weak zone at the ridge crest is simulated by the viscoelastic elements extending up to the surface beneath the immediate crest. Using a standard thermal and rheological model of the oceanic lithosphere, a normal ridge gives rise to horizontal deviatoric compression of about 40 MPa in the 25–30 km elastic layer beneath older ocean floor. A much smaller modelled compression of 9 MPa occurs in the 20 km thick elastic layer of the adjacent upper continental crust, as a result of the superimposed tension produced by the thick low-density continental crust (in reality this compression may be up to 30 MPa higher if the sub-continental mantle is denser than that beneath old ocean floor, as the geoid anomalies possibly suggest). A fourfold increase in spreading rate has an insignificant effect on the stresses. Much larger compressions develop adjacent to the modelled hot spot ridge in normal oceanic and especially continental lithosphere, these reaching 100 MPa beneath the old ocean floor and 90 MPa in the adjacent continent. The stresses determined by the modelling are comparable in magnitude but generally slightly lower than values estimated using the density moment function. The ridge push force referenced to 90 Ma old oceanic lithosphere is estimated to be 2.5 × 10 12 N/m for the modelled normal ridge and 6.2 × 10 12 for the modelled hot spot ridge. The modelling shows that the ridge push is produced by the high pressure and shear drag exerted by the asthenosphere on the lithosphere. The high pressure effect predominates at normal ridges where the plates are forced apart by gravitational wedging. The shear drag effect contributes substantially at hot spot ridges. The modelling helps to explain the prominent compressional stress in the continents bordering the North Atlantic, in terms of the hot spot activity beneath the mid-Atlantic ridge.