Abstract. In this work it is presented a computational model of a magnetic levitation system based on stacks of high-temperature second generation superconducting tapes (HTS) GdBa2Cu3O7-x. Сalculated magnetic field and the current distributions in the system for different stacks geometries in the zero-field cooling mode are also presented. The magnetization curves of the stacks in the external field of a permanent NdFeB magnet and the levitation force dependence on the gap between the magnet and the HTS tapes stack were obtained. A model of the magnetic system, oriented to levitation application, is given. Results of modeling were compared with the experimental data.