Obstructive Sleep Apnea (OSA) is a common respiratory disorder characterised by episodes of complete or partial obstruction of the upper airways during sleep. Nearly half of adults with OSA have comorbid Sleep Bruxism (SB), a condition in which a person grinds, gnashes, or clenches the teeth during sleep. However, sparse literature exists about the Finite Element Analysis (FEA) of mandibular advancement devices (MADs) for OSA therapy under a biting load. This manuscript presents a FEA to evaluate the effects of MADs (i.e., stress and displacement on periodontal ligaments and teeth) under a typical clenching load due to SB (i.e., 650 N), compared to the only OSA condition (baseline). Findings have demonstrated that the teeth stress and displacement are strictly related to the load magnitude and the MAD geometry (plateaux and relative position between the splints). Indeed, the applied load shifts the maximum values of stress and displacement from the MAD connecting sites to the contact area of the splints, increasing the stress in the anterior region of the maxilla. Despite this study being developed on one single patient and one single MAD model, this preliminary investigation can provide useful insights into the consequences of MAD usage in people affected by SB.