We propose a thermal-mechanical model of the rifting process that differs from previous models of lithospheric thinning (McKenzie, 1978; Sclater and Christie, 1980) by including the effect of the mechanical heterogeneity of the lithosphere. We divide the prerift continental lithosphere into ten horizontal mechanical layers that obey power-law creep. The ten layers are deformed in finite steps by extensile forces that remain constant at great distances from the rift. Power-law creep during extension causes necking of the lithosphere at mechanical instabilities beneath the rift axis. Thus, aesthenospheric upwelling is concentrated at an ever greater rate at the rift axis. We compute surface topography by assuming local isostatic compensation. At the rift axis, thinn ng of the crustal layers causes subsidence initially, but in some cases acceleration of aesthenospheric upwelling eventually causes thermal uplift late in the rifting process. This deformation sequence can explain the origin of one class of outer highs observed on passive continental margins (Schuepbach and Vail, 1980). Our model is consistent with data on mechanical properties of the lithosphere and with geological knowledge of rift valleys and passive margins. Furthermore, it satisfies our measurements of the scale and timing of formation of outer highs.