We use new and existing Bouguer gravity data to characterize the long-term flexural rigidity of the lithosphere beneath East Africa. Four tectonic provinces are characterized by distinct effective elastic plate thicknesses. These are the Tanzanian Craton, the Proterozoic Mobile Belts, the Paleogene rift basins in Sudan and Kenya, and the Cenozoic East African Rift System. Beneath the Tanzanian craton the elastic plate thickness is ~75 km, while the Pan African Mobile Belts and the Ubendian Belts are ~55 and ~65 km, respectively. The Paleogene rift basins exhibit an elastic plate thickness varying between 40 and 45 km. The effective elastic plate thickness within the faulted East African Rift System ranges from 14 km in the north to 33 km in the south. The minimum is found beneath the active rift of the Afar depression. The north to south along-rift axis variation in effective elastic plate thickness can be attributed to contrasts in the mechanical strength of the lithosphere. This is consistent with the north-south decrease in extensional velocity and the northward decrease in the focal depths of the earthquakes, reflecting a northward thinning in the brittle layer of the crust. The maximum elastic plate thickness is found beneath the Tanzanian craton, while the surrounding Mobile Belts have relatively moderate elastic plate thicknesses. The high effective elastic plate thickness of the Tanzanian craton suggests that this part of the lithosphere is rheologically competent compared to the surrounding Mobile Belts. The craton effectively resists deformation, even though it is located within a broad zone of an east-west extensional tectonic regime. Consequently, it has altered the direction of the rift propagation into the warmer and weaker lithosphere of the surrounding Mobile Belts.