We present a procedure for modeling the initially quasi-static upward progression of a zone of slip from some depth in the lithosphere toward the earth's surface, along a transform plate margin, culminating in a great crustal earthquake. Stress transmission in the lithosphere is analyzed with a generalized Elsasser model, in which elastic lithospheric plates undergo plane stress deformation and are coupled by an elementary foundation model to a Maxwellian viscoelastic asthenosphere. Upward progression of rupture over a finite length of plate boundary, corresponding to a seismic gap along strike, is analyzed by a method based on the 'line-spring' concept, whereby a two-dimensional antiplane analysis of the upward progression provides the relation between lithospheric thickness-averaged stress and slip used as a boundary condition in the generalized Elsasser plate model. The formulation results in a nonlinear integral equation for the rupture progression as a funtion of time and distance along strike. A simpler approximate single degree of freedom analysis procedure is described and shown to lead to instability results that can be formulated in terms of the slip-softening slope at the boundary falling below the elastic unloading stiffness of the surroundings. The results also indicate a delay of ultimate (seismic) instability due to the stiffer short versus long time asthenospheric response and predict a final period of self-driven creep toward instability. The procedures for prediction of rupture progression and instability are illustrated in detail for an elastic-brittle crack model of slip zone advance, and parameters of the model are chosen consistently with great earthquake slips and stress drops. For example, an effective crack fracture energy of the order 4¿106 J/m2 at the peak, 7 to 10 km below surface, of a Gaussian bell-shaped distribution of fracture energy with depth, with variance of the order 5 km, simulating strength build-up in a seismogenic layer, leads to prediction of nominal seismic stress drops of 30 to 60 bars and slips of 2 to 5 m in great strike slip earthquake ruptures breaking 100 to 400 km along strike. Precursory surface straining in the self-driven stage is predicted to proceed at a distinctly higher rate over time intervals begining 3 to 10 months before such an earthquake, this interval being greater for longer distances along strike over which the preseismic upward rupture progression takes place.