The Dead Sea rift is considered to be a plate boundary of the transform type. Several key questions regarding its structure and evolution are: Does sea floor spreading activity propagate from the Red Sea into the Dead Sea rift? Did rifting activity start simultaneously along the entire length of the Dead Sea rift, or did it propagate from several centres? Why did the initial propagation of the Red Sea into the Gulf of Suez stop and an opening of the Gulf of Elat start? Using crustal structure data from north Africa and the eastern Mediterranean and approximating the deformation of the lithosphere by a deformation of a multilayer thin sheet that overlies an inviscid half-space, the regional stress field in this region was calculated. Using this approach it is possible to take into account variations of lithospheric thickness and the transition from a continental to an oceanic crust. By application of a strain-dependent visco-elastic model of a solid with damage it is possible to describe the process of creation and evolution of narrow zones of strain rate localization, corresponding to the high value of the damage parameter i.e. fault zones. Mathematical simulation of the plate motion and faulting process suggests that the Dead Sea rift was created as a result of a simultaneous propagation of two different transforms. One propagated from the Red Sea through the Gulf of Elat to the north. The other transform started at the collision zone in Turkey and propagated to the south.