Using numerical thermo-mechanical experiments we analyze the role of an active mantle plume and pre-existing lithospheric-thickness differences in the structural development of the central and southern East African Rift system. The plume–lithosphere-interaction model setup captures the essential features of the studied area: two cratonic bodies embedded into surrounding lithosphere of normal thickness. The results of the numerical experiments suggest that localization of rift branches in the crust is mainly defined by the initial position of the mantle plume relative to the cratons. We demonstrate that development of the Eastern branch, the Western branch and the Malawi rift can be the result of non-uniform splitting of the Kenyan plume, which has been rising underneath the southern part of the Tanzanian craton. Major features associated with Cenozoic rifting can thus be reproduced in a relatively simple model of the interaction between a single mantle plume and pre-stressed continental lithosphere with double cratonic roots.