By making use of the empirical relations between stress and strain rate useful expressions concerning the variation of viscosity and activation energies for superplastic deformation are derived. The analyses of superplasticity, based on conventional continuum mechanics, neglect grain size effects. A new technique has been developed where the grain-size effect is incorporated into the rheological analysis. The analysis is subsequently made use of in understanding die-less drawing of superplastic bars. It is shown that the analysis is able to predict stress-strain rate relations, viscosity variation and so forth satisfactorily. It is concluded that the present analysis could be useful in practical situations where the constitutive equations are of great importance.