This study aimed to describe the displacement of anatomical structures and the stress distributions caused by the Hyrax, fan-type, and double-hinged expansion screws via the 3-dimensional (3D) finite element method (FEM). The 3D FEM was based on the computed tomography data of a 12-year-old patient with a constricted maxilla. The Hyrax model included 1,800,981 tetrahedral elements with 2,758,217 nodes. The fan-type model included 1,787,558 tetrahedral elements with 2,737,358 nodes. The double-hinged model included 1,777,080 tetrahedral elements with 2,722,771 nodes. The von Mises stress distributions after 0.2 mm of expansion and displacement patterns after 5 mm of expansion were evaluated. The highest stress accumulation was observed in the sutura zygomatico maxillaris area with all 3 appliances. An increase in stress was noted at the pterygomaxillary fissure, the medial and lateral pterygoid process of the sphenoid bone, and the nasal areas. The wedge-shaped skeletal opening was observed with all 3 appliances. In the transverse plane, maximum posterior expansion was achieved with the Hyrax appliance, whereas the maximum anterior expansion was observed with the double-hinged appliance. The maxilla moved inferiorly and anteriorly with all the 3 appliances. The greatest inferior displacement of the maxilla was recorded with the Hyrax appliance, whereas anterior maxillary displacement was the greatest with the double-hinged appliance. All the appliances showed similar stress distributions. The use of double-hinged screw caused a slight anterior displacement of point A. The fan-type and double-hinged appliances were shown to be more effective on anterior maxillary constriction, whereas the Hyrax appliance might be chosen for resolving maxillary posterior constriction.