Four specially designed surveys parallel to the Kermadec trench allow localized estimates of plate strength within the subducting Pacific plate to be made. The transfer function between topography and gravity is estimated for five trench-parallel ship tracks at distances of 25--110 km from the trench axis. We find a clear reduction in the magnitude and peak wavelength of the transfer function from the outer rise to the trench axis. The change in the transfer function indicates a decrease in plate strength and is consistent with a reduction in flexural rigidity by 3--5 orders of magnitude or a decrease in effective elastic thickness by more than 15 km. Such a large-magnitude decrease in the effective elastic strength suggests that the plate has little or no elastic strength within the trench and that viscous stresses play an important role in transferring slab-pull forces to the subducting plate and regulating plate speeds in subduction zones.