Mg-3Al-1Zn (AZ31) alloy was caliber rolled isothermally in the temperature range of 523 K to 723 K (250 °C to 450 °C) to develop fine grains of 3 to 13 µm. Tensile tests by constant initial strain rate as well as differential strain rate test techniques were conducted over the temperature range of 493 K to 723 K (220 °C to 450 °C) and strain rate range of 10−5 to 10−1 s−1. Maximum tensile elongation of 182 pct was obtained at test temperature of 723 K (450 °C) and strain rate of 10−3 s−1 in the sample obtained from caliber rolling at 723 K (450 °C), in spite of its large grain size of 13 µm. The strain rate sensitivity index ‘m’ was found to vary from 0.08 to 0.33 and activation energy for deformation ‘Q’ varied from 30 to 185 kJ mol−1 depending on test condition and caliber-rolling condition. These variations in m and Q values are explained by the difference in prior grain size, texture, and twins developed as a function of caliber-rolling temperature, and further by the concomitant microstructural change occurring during tensile test itself. The presence of twins and orientation of grains influences the parameters of the constitutive relation to varying extent. © 2015, The Minerals, Metals & Materials Society and ASM International.