A characterization of the responses of the Earth's crust to external perturbations is of fundamental importance for the estimation of seismograms as well as for the prediction of earthquakes. One set of such external perturbations are perturbations of the upper surface of tectonic plates either by wind stress or, for oceanic plates, by oceanic currents. In this paper, we extend the linear stability analysis of the Earth's crust in Brevdo  to studying destabilization of a model of a tectonic plate by wind stress. A plate of the Earth's crust is modelled as a horizontally homogeneous, vertically stratified, linearly visco-elastic waveguide of finite thickness and infinite horizontal extension rigidly attached to a solid half-space underneath it. Hooke's law extended by the Kelvin-Voigt damping model is assumed for the description of the visco-elastic properties of the plate. The upper free surface of the plate is supposed to be subjected to a constant wind stress. We apply an energy-type method to the normal-mode stability equations to show that a visco-elastic tectonic plate is destabilized by wind stress of a given strength provided that the internal friction damping in the plate is sufficiently low.