Here we use receiver function analysis to retrieve crustal thickness and crustal composition along the 35-My-old passive margin of the eastern Gulf of Aden. Our aims are to use results from the 3-D seismic array to map crustal stretching across and along the Aden margin in southern Oman. The array recorded local and teleseismic events between 2003 March and 2004 March. Seventy-eight events were used in our joint inversions for Vp/Vs ratio and depth. The major results are: (1) Crustal thickness decreases from the uplifted rift flank of the margin towards the Sheba mid-ocean ridge. We found a crustal thickness of about 35 km beneath the northern rift flank. This value decreases sharply to 26 km beneath the post-rift subsidence zone on the Salalah coastal plain. This 10 km of crustal thinning occurs across a horizontal distance of less than 30 km showing a localization of the crustal thinning below the first known rifted block of the margin. (2) A second rift margin transect located about 50 km to the east shows no thinning from the coast to 50 km onshore. The lack of crustal thickness variation indicates that the maximum crustal stretching could be restricted to offshore regions. (3) The along-strike variations in crustal structure demonstrate the scale and longevity of the regular along-axis rift segmentation. (4) Extension is still observed north of the rifted domain, 70 km onshore from the coast, making the width of margin larger than first expected from geology. (5) The crust has a felsic to normal composition with a probably strong effect of the sedimentary layer on the Vp/Vs ratio (comprised between 1.67 and 1.91).