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We describe a 3-D analytical model based on formal resolution of Maxwell's equations of a permanent-magnet linear actuator, with circular-shaped magnets. We present all details of the 3-D analytical calculation for the no-load flux and then compare results obtained by this model to those obtained by 3-D finite-element analysis. The comparisons show a good agreement between the two models and so validate our analytical model. Unlike 3-D finite-element analyses, which are time consuming, the analytical models that we present in this paper are suitable for an optimization process of such a structure. [ABSTRACT FROM AUTHOR]