Li- and Na-transition metal fluorosulfate materials (AFeSO4F, A=Li, Na) are proposed as highly promising novel cathode materials for Li- and Na-ion batteries. In this study, the electrochemical performance and elastic properties of AFe1-x M x SO4F (A=Li, Na; M=Co, Ni, Mg; x =0, 0.5, 1) are investigated from the view of first-principles calculations. The computational results reveal that the substitutions of Fe by Ni, Co and Mg enhance the intercalation voltage of the fluorosulphate materials. The density of states analysis shows that transition metal-doping AFeSO4F, especially for Ni doping case, could achieve better electronic conductivity in comparison with the pure phase and Mg-doped AFeSO4F. Further bader charges calculations give a confirmation that the Fe and Co in AFe0.5Co0.5SO4F play significant role in the charge transfer during delithiated or desodiated progresses, but the relatively inert character of Ni and Mg is discovered in AFe0.5Ni0.5SO4F and AFe0.5Mg0.5SO4F. LiFeSO4F and NaFeSO4F are found to be ductile from the exploration of elastic constants, whereas their delithiated and desodiated configurations have brittle character. In addition, Young’s Modulus (E), and Poisson's Ratio (ν) for LiFeSO4F, NaFeSO4F and 50% metal-doped AFe1-x M x SO4F (A=Li, Na; M=Co, Ni, Mg) are also presented to explore the hardness, bond characteristic and stability against shear.