We use the thin-sheet plane-stress approach to study the present-day dynamic behavior of the plate boundary between Eurasia and Africa along the Azores-Gibraltar region. This plate boundary, which extends from the Azores triple junction to the Gibraltar strait, shows a tectonic regime that changes from transtension in the west to transpression in the east, with a strike-slip motion in its central segment. Seismological data reveal that the western and central segments are currently marked by a linear series of earthquakes indicating that the plate boundary is located in a narrow zone. In contrast, the eastern segment is not so well defined and deformation spreads over a much broader area. To apply the thin-sheet approach, we combined heat flow, elevation and crustal thickness data to calculate the steady-state geotherm and the total strength of the lithosphere. Several models with different fault friction coefficients and geometries at the eastern segment of the plate boundary were tested. Results are compared with the maximum compressive stress directions from the World Stress Map, and the calculated seismic strain rates and slip vectors from earthquake data. The best fitting models are consistent with the rotation pole of Argus et al. [D.F. Argus et al., J. Geophys. Res. 94 (1989) 5585-5602], and show that the rheological behavior of the plate boundary must necessarily change from the western and central segments to the eastern segment. The diffuse character of the plate boundary east of the Gorringe Bank is dominated by the transition from oceanic to continental lithosphere, the weakness of the Alboran domain, and the convergence between the African and the Eurasian plates. The displacement of the Alboran domain relative to the African plate may play a major role in stress propagation through the Iberian Peninsula and its Atlantic margin.