The finite element method (FEM) is a computational method that can solve all biomechanical problems, including the field of orthodontics. The purpose of this virtual experimental study is to determine the behavior of a real orthodontic system subjected to different systems of loads. To analyze the real orthodontic system, we studied the case of a 21-year-old female patient. We used the InVesalius program, which can transform a set of DICOM-type images taken from cone beam computed tomography (CBCT) into three-dimensional structures. These structures were edited, modified, completed, and analyzed from a geometric point of view with the help of the Geomagic software. The final result of these operations must be a three-dimensional model made up of perfectly closed surfaces so that they can be transformed into virtual solids. The model consisting of perfectly closed surfaces is loaded into computer-aided design (CAD) programs. Bracket and tube components, as well as orthodontic wires, can be added to these models, similar to the analyzed patient’s tissues. When the model is complete and geometrically correct, it is exported to a program that uses FEM, such as Ansys Workbench. The simulation was performed for the forces of 0.5, 0.6, 0.7, 0.8, 0.9, and 1 N. The intention was to determine the behavior of the entire orthodontic system for these force values. After running the simulations, result maps were obtained that were composed of displacement, strain, and stress diagrams. It was also found that, in addition to the known rigidity, the orthodontic system has some elasticity due to the orthodontic wires, as well as the periodontal ligaments. Thus, a virtual analysis study can be carried out starting from a real patient with pre-treatment CBCT images and the virtual models of the bracket and tube elements and of the orthodontic wires.