Background: Rapid maxillary expansion (RME) has effects on the dental and periodontal structures of the parts involved, which vary according to the design and position of the expansion screw. The purpose of the study was to determine the optimal three-dimensional position of the Hyrax screw to obtain precise control of the dental movement and effect on the bone cortex using the finite element method (FEM). Material and Methods: RME was performed from the patient whom two Cone-Beam computerized tomography scans (CBCT) were obtained: T1 before expansion, and T2 three months after stabilization of RME. The FEM model was designed with T1 and of Hyrax photographs. FEM was obtained by comparing the simulation, T2, and clinical results. Three sagittal screw positions (anterior-middle-posterior) and vertical (upper-medium-low) were evaluated. Results: A coronal-buccal displacement of premolars and first molars was found which decreased in the occlusal-apical direction, presenting different types of dental movement in the screw positions; besides, a tendency of translational movement in the posterior-high location was observed. In the posterior-high position a higher concentration of efforts and homogeneous deformations in the periodontal ligament and vestibular cortex of the cervical area of first molars, first and second premolars were observed, with variations according to the screw position and the distribution of stresses. Conclusions: The ideal location of the expansion screw for controlling dental movement and periodontal side effects was the high-posterior position.