Aim To compare the effects of three different maxillary expansion appliances with five different types of expansion modalities on stress distribution and displacement on the maxilla and its adjacent craniofacial structures using the finite element method (FEM). Materials and methods Cone-beam computed tomography data of a patient with maxillary transverse deficiency were rendered into a three-dimensional model of craniomaxillary structures. The expansion appliances included tooth-borne, hybrid, and bone-borne expanders. Five different expansion modalities were applied to each expander [conventional Rapid Maxillary Expansion (RME) (type 1), midpalatal suture cortico-puncture-assisted RME (type 2), LeFort l cortico-puncture-assisted RME (type 3), surgically assisted RME (SARME) without pterygomaxillary junction (PMJ) separation (type 4), and SARME with bilateral PMJ separation (type 5)]. The numerical and visual data were analyzed. Results The highest amount of stress accumulation on teeth was found in the tooth-borne and hybrid groups. On the other hand, more stress concentration on the maxilla was observed in the bone-borne group. SARME cuts with PMJ separation increased total movement by reducing the stress on the midpalatal suture in all groups. While types 1, 2, and 3 were similar in terms of the amounts of displacement, types 4 and 5 increased the total amount of displacement in all groups. The total amounts of displacements from the highest value to the lowest value for the anterior and posterior maxilla were in the bone-borne, tooth-borne, and hybrid groups. Conclusions SARME cuts were effective in reducing stress on the teeth, but the cortico-puncture application affected neither the stress values on the teeth nor the transverse displacement in the tooth-borne expanders. Surgical procedures such as SARME and corticotomy should be used with bone-borne devices to improve the outcomes of maxillary expansion procedures.