Geodynamic models predict that rifting of thick, ancient continental lithosphere should not occur unless it is weakened by heating and magmatic intrusion. Therefore, the processes occurring along sections of the western branch of the East African Rift, where similar to 150 km thick, Palaeoproterozoic lithosphere is rifting with no surface expression of magmatism, are a significant challenge to understand. In an attempt to understand the apparently amagmatic extension we probed the regional uppermost mantle for signatures of thermal alteration using compressional (Vp) and shear (Vs) wave speeds derived from Pn and Sn tomography. Pervasive thermal alteration of the uppermost mantle and possibly the presence of melt can be inferred beneath the Rungwe volcanic centre, but no signatures on a similar scale were discerned beneath amagmatic portions of the western rift branch encompassing the southern half of the Lake Tanganyika rift and much of the Rukwa rift. In this region, Vp and Vs wave speeds indicate little, if any, heating of the uppermost mantle and no studies have reported dyking. Vp/Vs ratios are consistent with typical, melt-free, olivine-dominated upper mantle. Although our resolution limit precludes us from imaging potential localised magmatic intrusions with dimensions of tens of kilometres, the absence of surface volcanism, the amagmatic upper crustal rupture known to have occurred at disparate locations on the western branch, the presence of lower crustal seismicity and the low temperatures implied by the fast seismic wave speeds in the lower crust and uppermost mantle in this region suggests possible amagmatic extension. Most dynamic models predict that this should not happen. Indeed even with magmatic intrusion, rifting of continental lithosphere >100 km thick is considered improbable under conditions found on Earth. Yield strength envelopes confirm that currently modelled stresses are insufficient to produce the observed deformation along these portions of the rift system. Stresses arising from the gravitational force related to the uplift of the East African Plateau provide only one-eighth of the minimum stress necessary to produce observed lower crustal earthquakes in the western branch. We expect that some of this disparity may be accounted for by considering smaller scale bending stresses and dynamic feedbacks between brittle and elastic deformation and between faulting, topography and weathering that are not currently included in models of the East African Rift.