This article presents the development and validation of a three-dimensional force and torque semi-analytical model for ironless permanent magnet structures. This method relies on the definition of the magnetic flux density generated by permanent magnets in terms of elliptic integrals, allowing a fast computation when compared with finite element methods (FEM). The approach is validated and shown for two ironless passive magnetic bearing configurations by studying the applied force, torque and stiffness when small displacements and tilting are present.