The rolling direction (RD) and transverse direction (TD) of AM50 Mg alloy plate were drawn by tensile test while Digital Image Correlation (DIC) was applied to record local strain distribution and evolution. Then, the microstructure in the maximum strain position was observed so as to find the reason causing the difference between RD and TD specimen. Finally, the fracture surface morphology of the broken specimen was observed by scanning electron microscope (SEM) to determine the crack types. Through the analysis, it is found that the critical failure equivalent strains in the RD specimen and TD specimen are 0.1675 and 0.118, respectively, and the maximum equivalent strain position is the crack source; more twinning is generated in the RD specimen than that of the TD specimen, which indicates that twinning plays an important role in affecting its plasticity. The fracture surface morphology indicates that the RD specimen fracture is quasi-cleavage fracture while the TD specimen shows character of cleavage fracture.