Abstract: Based on the metallographical research results for the mechanism of super-plastic deformation, a costitutive relation of superplasticity of metal with uniform equiaxed fine grain is developed here by using the method of micro-cell model. The three micro-mechanism of superplastic deformation are included in the constitutive relation. An analysis of basic experimental phenomina of superplastic deformation, such as the influences of grain size and strain rate on stress-strain rate curve and strain rate sensiti...