It has been shown that a grain boundary may undergo two competing classes of elastic instability when the in-plane shear stress exceeds the proper critical values. It may buckle acquiring a sinusoidal shape or may develop a periodic series of fissures, separating bands with a sigmoidal profile. The two instabilities lead to grain sliding, but the corresponding expressions relating the relative velocity between adjacent grains with stress do differ. The plastic properties for small strains were calculated for the two force laws, which we called force models A and B. A comparison of the theoretical results with published experimental data shows that model A, while giving predictions within the experimental uncertainties for a series of superplastic aluminium and titanium alloys, fails for Avesta 2304 steel. However, excellent results are obtained when model B is applied for this steel.