A finite element model of extension in the continental lithosphere shows that, on the U.S. Atlantic margin, the presence of pre-existing weaknesses within the lithosphere can account for variations in subsidence and extension, hinge zone development and some aspects of magmatic activity during rifting. The lithosphere is treated as a layered viscoplastic material consisting of a quartz diorite crust and dunite mantle. The crustal weakness may result from thrust faulting during the Paleozoic Appalachian orogeny, and is treated as a region within the crust with a weaker rheology. The mantle weakness results from thickening of the crust below the pre-rift Appalachian orogen. The model indicates that subsidence in the early stages of rifting is focused in the region encompassing the crustal weakness. at the location where the Triassic rift basins formed at about 225-195 Ma. Extension within the mantle during this stage of rifting is diffuse, and a shear zone develops within the lower crust connecting the crustal weakness to the mantle weakness, in a manner akin to simple shear. As rifting continues, extension within the mantle becomes focused in a narrow region under the mantle weakness. The crust above the mantle weakness is thermally weakened, and the locus of subsidence and crustal extension shifts to the region overlying the mantle weakness. The style of extension from this time onward is similar to pure shear. Seafloor spreading ultimately develops over the position of the original mantle weakness at about 175 Ma. The model accounts for a number of hitherto unexplained features of the U.S. Atlantic margin, including the shifting of the locus of extension from the Triassic basins to the deep offshore basins, hinge zone development, timing and position of magmatic activity. the location of the initiation of seafloor spreading, and the asymmetry of the conjugate margins of the rift. The predicted shift from simple shear to pure shear rifting style may be a characteristic of other continental rifts and passive margins.