The aim of this study was to investigate whether the polymer polyether ether ketone (PEEK), which is approved for (dental) medical appliances, is suitable for the production of orthodontic treatment appliances. Different geometries of transpalatal arches (TPAs) were designed by Computer Aided Design (CAD). Out of a number of different designs and dimensions, four devices were selected and manufactured by milling out of PEEK. A finite element analysis (FEA) and a mechanical in vitro testing were performed to analyze the force systems acting on the first upper molars. Up to an activation (transversal compression) of 4 mm per side (total 8 mm), the PEEK TPAs generated forces between 1.3 and 3.1 Newton (N) in the FEA and between 0.7 and 3.2 N in the mechanical testing. The moments in the oro-vestibular direction were measured between 2.1 and 6.6 Nmm in the FEA and between 1.1 and 6.0 Nmm in the mechanical testing, depending on the individual TPA geometry. With the help of the FEA, it was possible to calculate the von Mises stresses and the deformation patterns of the different TPAs. In some areas, local von Mises stresses exceeded 154–165 MPa, which could lead to a permanent deformation of the respective appliances. In the in vitro testing, however, none of the TPAs showed any visible deformation or fractures. With the help of the FEA and the mechanical testing, it could be shown that PEEK might be suitable as a material for the production of orthodontic TPAs.