Abstract Crustal and upper-mantle structure of major units of the Afro-Arabian rift system has been progressively investigated by seismic-refraction surveys in the Jordan-Dead Sea rift, the Red Sea, the Afar depression and in the East African rift of Kenya. The two extreme structures are oceanic crust flooring the axial trough of the southern Red Sea rift and 30–35 km thick continental crust underneath the Jordan-Dead Sea rift and its flanks underlain by a mantle with Pn-velocities of 8.0–8.2 km/s. The remainder of the units have a crustal structure of transitional to uncertain nature. In the southeastern Red Sea, the change from 15–18 km thick transitional crust to the 40 km thick continental crust of the Arabian Shield is probably very abrupt and is the major lateral change in structure in this region. In the northern Afar depression, the crust is only 15–20 km thick. In the southern Afar depression, anomalous mantle with 7.2–7.3 km/s velocities occurs at depths greater than 25 km. Also here, an abrupt change to a 40 km thick shield crust with a velocity of 8.0 km/s is evident from seismic and gravity data. Crustal thickness of the East African rift system amounts to 30–36 km. A recent trial experiment in the eastern rift of Kenya indicates a 35–36 km thick crust underlain by a low-velocity upper mantle with 7.5 km/s. At 23–24 km depth a thin high-velocity lens of 7.1 km/s velocity may be present within the 22 km thick lower crustal layer averaging 6.6 km/s velocity. Investigations of local earthquake body waves in the western rift provide information that the crust here is of continental type with a thickness of about 32 km overlying mantle material of 8.0 km/s P-velocity and 4.6 km/s S-velocity. In conclusion, a model of preferential rifting of continents is applied to the Afro-Arabian rift system where rifting seems to progress into areas with thick continental crust as seen for example in the Levant and the East African rift systems instead of using paths in thin crust.