Dynamic modeling of continental extension between South America and Africa shows that the mechanics of rifting played an important role in determining the pattern of volcanism within the Paraná and Etendeka flood-basalt provinces on the Brazilian and Namibian margins. The key feature of the model is the development of a horizontal pressure gradient in the lower crust during the early stages of extension, which provided a mechanism for transporting magma generated beneath the incipient sea-floor spreading axis into the Paraná province, 100-200 km distant. The horizontal pressure gradient developed as a consequence of the dynamic interaction of preexisting weaknesses in the middle crust and upper mantle during rifting. The model accounts for the large quantity of basalt, the asymmetric distribution of basalt on the conjugate margins, and the northward migration of the eruptive center with time. The rapidity of magma genesis is in agreement with models of decompression melting during rifting. The model indicates that although elevated asthenosphere temperatures associated with the Tristan plume account for the volume of melt generated, the mechanics of rifting control the location and style of emplacement. The model suggests that extension in the region began ca. 150-155 Ma, and lasted about 25 m.y.