We present a model for the effect of stress on thin amorphous films that develop atop ion-irradiated silicon, based on the mechanism of ion-induced anisotropic plastic flow. Using only parameters directly measured or known to high accuracy, the model exhibits remarkably good agreement with the wavelengths of experimentally-observed patterns, and agrees qualitatively with limited data on ripple propagation speed. The predictions of the model are discussed in the context of other mechanisms recently theorized to explain the wavelengths, including extensive comparison with an alternate model of stress.