Stacks of large width superconducting tape can carry persistent currents over similar length scales to bulk superconductors, therefore giving them potential for trapped field magnets and magnetic levitation. 46 mm wide high temperature superconducting tape has previously been cut into square annuli to create a 3.5 T persistent mode magnet. The same tape pieces were used here to form a composite bulk hollow cylinder with an inner bore of 26 mm. Magnetic levitation was achieved by field cooling with a pair of rare-earth magnets. This paper reports the axial levitation force properties of the stack of annuli, showing that the same axial forces expected for a uniform bulk cylinder of infinite $J\; c$ can be generated at 20 K. Levitation forces up to 550 N were measured between the rare-earth magnets and stack. Finite element modelling in COMSOL Multiphysics using the H-formulation was also performed including a full critical state model for induced currents, with temperature and field dependent properties as well as the influence of the ferromagnetic substrate which enhances the force. Spark erosion was used for the first time to machine the stack of tapes proving that large stacks can be easily machined to high geometric tolerance. The stack geometry tested is a possible candidate for a rotary superconducting bearing.