In this study we image crustal structure beneath a magmatic continental rift to understand the interplay between crustal stretching and magmatism during the late stages of continental rifting: the Main Ethiopian Rift (MER). The northern sector of this region marks the transition from continental rifting in the East African Rift to incipient seafloor spreading in the southern Red Sea and western Gulf of Aden. Our local tomographic inversion exploits 172 broad-band instruments covering an area of 250 x 350 km of the rift and adjacent plateaux. The instruments recorded a total of 2139 local earthquakes over a 16-month period. Several synthetic tests show that resolution is good between 12 and 25 km depth (below sea level), but some horizontal velocity smearing is evident along the axis of the Main Ethiopian Rift below 16 km. We present a 3-D P-wave velocity model of the mid-crust and present the first 3-D Vp/Vs model of the region. Our models show high P-wave velocities (6.5 km s(-1)) beneath the axis of the rift at a depth of 12-25 km. The presence of high Vp/Vs ratios (1.81-1.84) at the same depth range suggest that they are cooled mafic intrusions. The high Vp/Vs values, along with other geophysical evidence, suggest that dyking is pervasive beneath the axis of the rift from the mid-crustal depths to the surface and that some portion of partial melt may exist at lower crustal depths. Although the crustal stretching factor across the Main Ethiopian Rift is similar to 1.7, our results indicate that magma intrusion in narrow zones accommodates a large proportion of extensional strain, with similarities to slow-spreading mid-ocean ridge processes.