Lithospheric breakup is, in general, oblique to the principal strain axes, with shortening in one horizontal axis (eh<0). Local necking of the plate, including the mantle part of the lithosphere, is necessary for the creation of a divergent plate boundary. The necking developes as a mechanical instability that decreases the resistance of the plate to extension despite the intrinsic hardening of the material. We model the flow that precedes breakup stressing two aspects that have been overlooked before: (1) three-dimensional flow, and (2) strain dependent strength of the lithosphere. The model mimics spatial and temporal features of the most extensively documented rift systems. The neck is oblique to the direction of principal extension, and the transition from diffuse stretching to local necking is abrupt at 5--10% strain. The critical strain for local necking in the model appears to be independent of the intrinsic strength. Therefore various rheological layers (brittle upper crust, ductile lower crust, and stiffer but hotter mantle lithosphere) may neck concomitantly to form a rift.