We present coseismic slip and afterslip inversion models based on the same fault geometry for the M-w 8.6 2005 Nias-Simeulue earthquake at the Sumatran subduction zone. We estimate the coseismic slip using near-field static GPS offsets, and vertical displacements based on satellite and coral data, while we estimate the afterslip simultaneously with viscoelastic flow using approximately nine years of GPS data following the event. With the current spatial resolution of our GPS network it is difficult to accurately resolve contributions from different postseismic mechanisms, that is, afterslip and viscoelastic relaxation from oceanic or continental mantle. We thus run many synthetic tests and models with various setups to find features that consistently appear in all our models, which we consider as robust. We find that the estimated afterslip is located primarily updip and downdip of the coseismic rupture patch and partially overlaps the updip region of the coseismic slip. We also find that the viscoelastic flow in the mantle wedge following this event was likely localized beneath the downdip region of the coseismic slip, rather than uniformly layered across the area as assumed by forward models. This localized viscoelastic flow coincides with a low-velocity zone below Toba volcano, as imaged by tomography studies; it is possible that the viscoelastic flow beneath the volcano accelerated following this event.