Magnesium alloys are a popular research topic for structural applications because they have a lower density than conventional structural materials, including steel, titanium, and aluminum; however, the reliability and safety of their mechanical properties must be further proven. An important mechanical property for this purpose is fracture toughness, which is the measure of the material's resistance to crack propagation. In this study, a model of an experiment to investigate the fracture toughness of a magnesium alloy WE43 before and after friction stir processing (FSP) is developed, and the results are compared to those produced by a digital image correlation (DIC) system during an experiment from another paper. The model results of the material before FSP matched well with the DIC results, but the model of the material after FSP only partially matches the DIC results. In addition, a theoretical approach to calculating the standard fracture toughness value, KIc, from the modeling results is proposed, and is found to be a conservative approach.