Rapid maxillary expansion is employed for the treatment of cross-bite and deficiency of transversal dimension of the maxilla in patients with and without cleft of palate and lip. The aim of this study is the finite-element analysis of stresses and displacements of skull, with and without unilateral cleft, after application of the HYRAX orthodontic device. Three different constructions of the orthodontic Hyrax device with different positions of the screw-in the occlusal horizontal plane, near occlusal horizontal plane and near the palate-are considered. Application of the orthodontic device corresponds to the rotation of the screw on one-quarter turn. It is established that the screw position significantly affects the stress patterns in skull and displacements of the cranium with and without unilateral palate cleft. Depending on the construction of the orthodontic appliance, the maxilla halves in the transversal plane are unfolded or the whole skull is entirely rotated in the sagittal plane. The obtained results can be used for designing of orthodontic appliances with the Hyrax screw, as well as for planning of osteotomies during the surgical assistance of the rapid maxillary expansion.