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In this paper we present calculations of levitation forces between a cylindrical permanent magnet and a cylindrical superconductor using a commercial finite element program. Force limits for zero field cooled and field cooled processes have been obtained using the Meissner effect and the perfect pinning hypothesis, respectively. Comparison of the experimentally determined forces with respect to these limits provides a simple estimation of the sample quality. The hysteretical behavior of the forces has been reproduced assuming a critical state model for the superconductor. Results are compared with experimental data. Excellent agreement has been found for forces measured after zero field cooled process thus allowing us to estimate the critical current of the samples. As a further exploitation of the software capabilities we have investigated the effects of the superconducting sample geometry and the effects of different strategies of flux conditioning to optimize the levitation forces. © 1997 American Institute of Physics.