In this work we use the thin-shell approximation to model the neotectonics of the western part of the Africa–Eurasia plate boundary, extending from the Mid-Atlantic ridge to Tell Atlas (northern Algeria). Models assume a nonlinear rheology and include laterally variable heat flow, elevation, and crust and lithospheric mantle thickness. Including the Mid-Atlantic ridge permits us to evaluate the effects of ridge push and to analyse the influence of the North America motion on the area of the Africa–Eurasia plate boundary. Ridge push forces were included in a self-consistent manner and have been shown to exert negligible effects in the neotectonics of the Iberian Peninsula and northwestern Africa. Different models were computed with systematic variation of the fault friction coefficient. Model quality was scored by comparing predictions of anelastic strain rates, vertically integrated stresses and velocity fields to data on seismic strain rate computed from earthquake magnitude, most compressive horizontal principal stress direction, and seafloor spreading rates on the Mid-Atlantic ridge. The best model scores were obtained with fault friction coefficients as low as 0.06–0.1. The velocity boundary condition representing spreading on the Mid-Atlantic ridge is shown to produce concentrated deformation along the ridge and to have negligible effect in the interior of the plates. However, this condition is shown to be necessary to properly reproduce the observed directions of maximum horizontal compression on the Mid-Atlantic ridge. The maximum fault slip rates predicted by the model are obtained along the Mid-Atlantic ridge, Terceira ridge and Tell Atlas front. Relatively high slip rates are also obtained in the area between the Gloria fault and the Gulf of Cadiz. We infer from our modelling a significant long-term seismic hazard for the Gloria fault, and interpret the absence of seismicity on this fault as possibly due to transient elastic strain accumulation. The present study has also permitted better understanding of the geometry of the Africa–Eurasia plate boundary from the Azores triple junction to the Algerian Basin. The different deformational styles seem to be related to the different types of lithosphere, oceanic or continental, in contact at the plate boundary.