Relaxation following large subduction earthquakes produces landward changes in surface velocities. Near-trench landward velocity changes in the vicinity of the rupture zone have been attributed to rapid viscoelastic relaxation in the sub-slab asthenosphere. Lateral landward velocity changes, hundreds of km along-trench from the rupture, have been variously explained invoking interplate coupling changes, transient slab acceleration, or overriding plate bending, with different implications for seismic hazard. We investigate whether the lateral landward velocity changes can result from postseismic relaxation with constant interplate coupling and convergence rate. We use a finite element model with periodic megathrust earthquakes resulting from unlocking of asperities on the megathrust, with instantaneous, dynamically driven coseismic slip and afterslip and with bulk visco-elastic relaxation. A mechanical contrast in the overriding plate is required to reproduce the observed near-trench focusing of interseismic deformation. A maximum depth limit to afterslip of around 100 km is consistent with inverted afterslip distributions and the hypothesized depth extent of the megathrust. The presence of both the contrast and depth limit causes viscous relaxation in the mantle wedge to result in lateral landward velocity changes. We discuss the responsible mechanism, which amounts to elastic deformation of the overriding plate and is due to the finite compressibility of the plate and its in-plane bending. The spatial pattern of landward velocity changes is consistent with observations for the Maule and Tohoku earthquakes. Velocity change magnitudes are comparable with observations, scale with viscosity and seismic moment, are only partly counteracted by the effect of primary afterslip, and are little affected by interplate coupling pattern. In the years following the largest earthquakes with rapidly decaying afterslip, this mechanism is expected to produce detectable landward velocity changes. The models also shows near-trench landward velocity changes close to the rupture, consistently with previous research. However, we find that the extent and timing of shallow interface (re)locking is critical for reproducing near-trench observations on the overriding plate.