Titanium fixation devices are the gold standard for the treatment of mandibular fractures; however, they present serious limitations, such as non-degradability and generation of imaging artifacts. As an alternative, biodegradable magnesium alloys have lately drawn attention due to their biodegradability and biocompatibility. In addition, magnesium alloys offer a relatively high modulus of elasticity in comparison to biodegradable polymers, being a potential option to substitute titanium in highly loaded anatomical areas, such as the mandible. This study aimed to evaluate the biomechanical competence of magnesium alloy WE43 plates for mandibular fracture fixation in comparison to the clinical standard or even softer polymer solutions. A 3D finite element model of the human mandible was developed, and four different fracture scenarios were simulated, together with physiological post-operative loading and boundary conditions. In a systematic comparison, the material properties of titanium alloy Ti-6Al-4V, magnesium alloy WE43, and polylactic acid (PLA) were assigned to the fixation devices, and two different plate thicknesses were tested. No failure was predicted in the fixation devices for any of the tested materials. Moreover, the magnesium and titanium fixation devices induced a similar amount of strain within the healing regions. On the other hand, the PLA devices led to higher mechanical strains within the healing region. Plate thickness only slightly influenced the primary fixation stability. Therefore, magnesium alloy WE43 fixation devices seem to provide a suitable biomechanical environment to support mandibular fracture healing in the early stages of bone healing. Magnesium WE43 showed a biomechanical performance similar to clinically used titanium devices with the added advantages of biodegradability and radiopacity, and at the same time it showed a remarkably higher primary stability compared to PLA fixation devices, which appear to be too unstable, especially in the posterior and more loaded mandibular fracture cases.