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The results of numerical and experimental analysis of passive magnetic bearings are presented. The proposed structure is composed of three radially stacked ring-shaped permanent magnets. The improvements of stiffness and load capacity are proven in comparison to the classical passive magnetic bearing composed of two rings. A preliminary sensitivity analysis is carried out by means of the 2-dimensional finite element method (FEM) modelling, which is used to provide the initial points for the stochastic optimisation and also to define the best fitness and penalty functions. Finally, the 2-dimensional FEM is used to compare the force density and the cost of the proposed structure to those of the classical passive magnetic bearing composed of two rings. The optimised structure was manufactured and validated by experimental measurements. The proposed passive magnetic bearing exerts greater axial force and stiffness than similar structures. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.