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Background: Although titanium plates/screws are effective fixation methods (FM) after L-shaped osteotomy reduction malarplasty (LORM), the ideal FM remains controversial. This first finite element analysis (FEA) aimed to study the effect of various zygomatic body/zygomatic arch FM combinations and their placement vectors on the zygoma complex stability after virtual LORM under the effect of both average (150 N/mm2) and maximum (750 N/mm2) forces and three-dimensional (3D) mapping of stress and strain parameters distribution over the zygomatic bone, fixation methods, and total model. Results: The fixation methods about the short-arm of the L-shaped osteotomy showed lower stress, strain, and displacement values than those across the long-arm osteotomy site. Combined with any zygomatic arch fixation methods (ZAFm), the two bicortical screws group (2LS) on the zygomatic body osteotomy site resulted in smaller displacements and the lowest zygoma bone stress and displacement when combined with Mortice–Tenon structure (MT) as zygomatic arch fixation method. Applied forces caused statistically significant differences in zygomatic bone stress (P < 0.001 and P = 0.001) and displacement (P = 0.001 and P = 0.002). Conclusion: All FMs both on the zygomatic body and zygomatic arch provide adequate zygomatic complex stability after LORM. The 2LS group showed better resistance than rectangular plate (RP) and square plate (SP) with lower stress concentrations. The L-shaped plate with short-wing on the maxilla (LPwM) is more stable than having the short-wing on the zygoma bone (LPwZ). Future prospective clinical studies are required to validate the current findings. [ABSTRACT FROM AUTHOR]