We formulate a mechanical model describing the formation of rifts as finite amplitude necking of an elastic-plastic layer overlying a fluid substrate. A perfectly plastic rheology is a continuum description of faulting in rift zones. Two important aspects of rift evolution are illustrated by this model: the evolution of the rift width as extension proceeds and the finite strain that occurs. A region at yield initially develops with a width determined by the thickness of the brittle layer, and the internal deformation within this yield zone is proportional to the topographic slope. An extension proceeds, the surface within the rift subsides, and the width of the subsiding yield zone decreases. At any stage of rifting, material in regions just outside the yield zone is deformed but no longer deforming. The width of these deformed regions increases with increasing extension. Vertical forces due to the mass deficit of the rift depression will flex the elastic layer outside the yield zone, creating flanking uplifts. The external force required to maintain active rifting increases with the amount of lithospheric stretching, indicating that rifting is a quasi-static, stable process. Because the yield zone will revert to elastic behavior if the external force causing extension is removed, the model predicts that the rift depression and flanking uplifts will be preserved after extension stops. Our simple mechanical model demonstrates the inherent relationship among graben formation, lithospheric thinning, and rift shoulder uplift in rift zones. ¿ American Geophysical Union 1990