This paper presents a simple quantitative model for the transfer of lithospheric extension along deep crustal shear zones during rifting of continents. These shear zones are interpreted to connect laterally offset pre-existing weaknesses in the crust to the centre of mantle lithospheric thinning, the rift axis. For quartz and quartz-over-feldspar dominated crustal models, we predict the formation of major crustal shear zones which transfer extension to offset crustal weak zones as much as several hundreds of kilometres from the rift axis. The length scale of this transfer depends on the initial thermal regime of the lithosphere, the composition and thickness of the crust, and the relative strengths of the crust at the rift axis and in the offset weak zones. When rifting results from a combination of in-plane tensile stress and active heating of the mantle lithosphere from below, the lateral transfer of strain occurs for a period of time early in the rifting process. Later, crustal thinning switches to the rift axis because heat diffusing from below weakens the crust at this location and it is no longer energetically preferable to transfer strain to offset weak zones. For the parameter values used in our models, the sedimentary basins formed by extension at the offset weak zones remain tectonically active for no more than 10 My. Transfer of strain to the offset, or rift flank, basins is most efficient when the rate of active heating of the lithosphere is similar to the rate of deformation along the crustal shear zone. Results from a more complete plane-strain finite element model agree with the basic predictions of the simple quantitative model. They do, however, indicate that effects ignored in the simple model will reduce our estimates of the maximum distance of shear transfer. This is particularly true when the deformation is large. We interpret sedimentary basins located on the flanks of rifts or Atlantic-type margins to be the products of this process of strain partitioning in an inhomogeneous lithosphere. The models provide an explanation for flank or offset basins that were active for a short interval early in a rift phase, that have no thermal subsidence phase and that cannot be attributed to the gravitationally driven extension and collapse of orogenically overthickened crust.