A long section of the Sunda megathrust south of the great tsunamigenic earthquakes of 2004 and 2005 is well advanced in its seismic cycle and a plausible candidate for rupture in the next few decades. Our computations of tsunami propagation and inundation yield model flow depths and inundations consistent with sparse historical accounts for the last great earthquakes there, in 1797 and 1833. Numerical model results from plausible future ruptures produce flow depths of several meters and inundation up to several kilometers inland near the most populous coastal cities. Our models of historical and future tsunamis confirm a substantial exposure of coastal Sumatran communities to tsunami surges. Potential losses could be as great as those that occurred in Aceh in 2004.