The superplastic deformation behaviour of a two-dimensional nonequiaxed microstructure is investigated on the basis of the grain-rolling mechanism proposed by Paidar and Takeuchi for an equiaxed microstructure. Analysis shows that not only the deformation geometry but also the dynamics of grain boundary dislocation activity will be altered if grains are elongated rather than equiaxed. Constitutive equations thus derived indicate that the grain aspect ratio can impose a remarkable influence on the superplastic stress-strain rate relationship and such an influence can be quite different if the orientation of the applied stress lies over an angle with respect to the longer axis of the grains. The complexity of modelling the superplastic deformation of engineering materials is also discussed.