The 26 December 2004 Mw = 9.2 and 28 March 2005 Mw = 8.7 earthquakes on the Sumatra megathrust altered the state of stress over a large region surrounding the earthquakes. We evaluate the stress changes associated with coseismic and postseismic deformation following these two large events, focusing on postseismic deformation that is driven by viscoelastic relaxation of a low-viscosity asthenosphere. Under Coulomb failure stress (CFS) theory, the December 2004 event increased CFS on the future hypocentral zone of the March 2005 event by about 0.25 bar, with little or no contribution from viscous relaxation. Coseismic stresses around the rupture zones of the 1797 and 1833 Sunda trench events are negligible, but postseismic stress perturbations since December 2004 are predicted to result in CFS increases of 0.1 to 0.2 bar around these rupture zones between 2 and 8 years after the December 2004 event. These are considerable stress perturbations given that the 1797 and 1833 rupture zones are likely approaching the end of a complete seismic cycle.