The levitation force and stability of superconducting levitation devices are strongly dependent on both the geometry and dimensions of the components and the cooling process of the superconductor. In this work we study these effects in levitating systems consisting of an infinitely long superconductor and a guideway of different arrangements of infinitely long parallel permanent magnets. Using a model based on the critical-state model and a magnetic-energy minimization procedure, taking into account the demagnetization fields, we analyze the influence of parameters of the system such as the width and height of the superconductor and those of the permanent magnets on the levitation force and stability for two different cooling processes, field cooling and zero-field cooling. The theoretical predictions are compared with existing experimental data. From the results obtained, we provide some general trends on how the dimensions of the components of maglev systems could be chosen to improve both the levitation force and the stability. © 2008 IOP Publishing Ltd.