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Abstract: Pull-apart basins are depressions that form as the result of crustal extension along strike-slip systems where the sense of fault stepping or bending coincides with that of fault slip. They are common features of strike-slip systems. We perform a number of numerical thermomechanical experiments to explore how the rheology of the lithosphere influences basin evolution and lithospheric structure beneath the basin. Our modeling shows that basin subsidence results from the competition of extension of the brittle part of the lithosphere, which leads to its subsidence, and of the compensating flow of the deeper ductile part of the lithosphere, which pushes the extended brittle block upwards. The result of this competition is the subsidence rate. Strain partitioning beneath the basin and crustal structures is controlled by (i) the thickness of the brittle layer and basin width, (ii) the magnitude of strike-slip displacement, (iii) the rate of frictional softening of the crust, and (iv) the viscosity of the ductile part of the lithosphere. The thickness of the brittle layer and the viscosity of the underlying ductile part of the lithosphere in turn depend on temperature, composition and material softening. We interpret the modeling results, deducing simple analytical expressions based on the “brittle brick stretching” (BBS) approach, which despite its simplicity describes the structure and evolution of pull-apart basins reasonably well. We also demonstrate that the structure and evolution of the Dead Sea Basin, located at a left step of the Dead Sea Transform in the Middle East, is consistent with a BBS type of deformation with only a minor contribution from compensational flow in the ductile part of the lithosphere. Finally, we show that the formation of a deep narrow pull-apart basin in relatively cold lithosphere, as in the Dead Sea Basin, requires very low friction at major faults (lower than 0.1–0.2). If this condition is not satisfied, strike-slip deformation does not localise and deep basins do not form. [Copyright &y& Elsevier]