Fine grains were developed in Mg-3Al-1Zn (AZ31) alloy by isothermal Caliber Rolling (CR) at five different temperatures in the range of 250-450°C. The samples of different grain sizes were deformed by constant strain rate (CSR) and differential strain rate (DSR) test techniques over the temperature range of 220-450 °C and strain rate range of 10-5 to 10-1 s-1. The effects of grain size, test temperature and strain rate on flow stress were analysed to develop the constitutive relationship for superplastic deformation. © (2013) Trans Tech Publications, Switzerland.