In-plane horizontal stresses acting on predeformed lithosphere induce differential flexural vertical motions. A high-precision record of these motions can be found in the sedimentary record of rifted basins. Originally, it was proposed that rifted basins experience flank uplift and basin center subsidence in response to a compressive change of in-plane stress, which agrees well with observed differential motions. Subsequently published models predicted that the vertical motions may be opposite because of the flexural state of the lithosphere induced by necking during extension. However, the total, flexural and permanent, geometry of the lithosphere underlying the rifted basin is the controlling parameter for the in-plane stress-caused vertical motions. The largest part of this preexisting geometry is caused by faulting in the uppermost brittle part of the crust and ductile deformation in the underlying parts of the lithosphere. We present a new multilayered model for stress-induced differential subsidence, taking into account the tectonically induced preexisting geometry of the lithosphere, including faults in the upper crust. As continental lithosphere may exhibit flexural decoupling due to a weak lower crustal layer, the new multilayer in-plane stress model discriminates the geometries of the separate competent layers. At a basin-wide scale, the new model predicts that a compressive change of in-plane force results in basin center subsidence and flank uplift, confirming the original hypothesis. Compared to all previous models, the new model requires a lower horizontal stress level change to explain observed differential vertical motions. ¿ 1998 American Geophysical Union