Abstract The initiation of the Afro-Arabian Rift System on three nearly straight segments occurred shortly after massive amounts of basalt poured out of the triple junction of those segments in Afar. The synchroneity of magmatism and rifting may reflect the fact that normal continental lithosphere is too strong to rift without magmatic dyke intrusions and the straightness of rifts reflects a localized source for the magma feeding those dykes. Simple relations are derived for the minimum extensional force needed for lithosphere cutting dyke intrusions as functions of the density structure and thickness of the lithosphere. As long as the density contrast between continental crust and magma is small compared to the density contrast between the mantle and magma, then the force needed to rift scales with the square of the thickness of the mantle lithosphere. Thus, continental regions with normal-thickness lithosphere may rift when reasonable levels of extensional force and sufficient magma are available. Very thick mantle lithosphere may not rift at levels of force that are likely to arise on Earth. Two main sections of the Afro-Arabian Rift System, the Red Sea and the Ethiopian Rift, appear to have developed as magma-assisted rifts in normal continental lithosphere. The northern and southern ends of the system are bounded by regions of very thick mantle lithosphere where dykes could not open. In the south, the Tanzanian Craton, with normal-thickness crust and a very deep lithospheric root, was also not split by the rift. In the north, the rift opened along a nearly straight line from the centre of the flood basalt province 2000 km to the edge of the Mediterranean Sea. The old oceanic lithosphere of this margin may be no thicker than the adjacent continental lithosphere of Egypt, but the thinner oceanic crust means that Mediterranean lithosphere may be too thick and dense to rift magmatically. The role of magma in the third branch, the Gulf of Aden, is not so clear given the lack of syn-rift dykes.