We analyze the observed dynamic slip transfer from the Denali to Totschunda faults during the Mw 7.9 3 November 2002 Denali fault earthquake, Alaska. This study adopts the theory and methodology of Poliakov et al. (2002) and Kame et al. (2003), in which it was shown that the propensity of the rupture path to follow a fault branch is determined by the preexisting stress state, branch angle, and incoming rupture velocity at the branch location. Here we check that theory on the Denali-Totschunda rupture process using 2D numerical simulations of processes in the vicinity of the branch junction. The maximum compression direction with respect to the strike of the Denali fault near the junction has been estimated to range from approximately 73° to 80°. We use the values of 70° and 80° in our numerical simulations. The rupture velocity at branching is not well constrained but has been estimated to average about 0.8 cs throughout the event. We use 0.6 cs , 0.8 cs , 0.9 cs , and even 1.4 cs as parameters in our simulations. We simulate slip transfer by a 2D elastodynamic boundary integral equation model of mode II slip-weakening rupture with self-chosen path along the branched fault system. All our simulations except for 70° and 0.9 cs predict that the rupture path branches off along the Totschunda fault without continuation along the Denali fault. In that exceptional case there is also continuation of rupture along the Denali fault at a speed slower than that along the Totschunda fault and with smaller slip.