Passive magnetic bearings (PMB) is a new concept of flywheel energy storage systems in which conventional bearings are replaced by magnetic bearings while keeping the rest parts unchanged to increase the rotating speed of the flywheel and while reducing the vibrations of the system. This paper presents the FEM analysis of a several design solutions for PMB. The aim is to compare several design solutions. In this study we used the magnetic scalar potential formulation for the magnetic field problem. This approach allows for relative fast numerical solution, useful in computing the magnetic forces of interest in the PMB design. The forces are computed using the theorem of the generalized forces, a method consistent with the scalar potential formulation (the power losses are neglected). The results conclude the different PMBs performances. This paper is concerned with the optimization of a Halbach array type PMB (4), and the evaluation of design parameters such as the magnetic forces and stiffness. Four PMB models were CAD designed (5). The magnetic field models were solved by the finite element method (FEM) (6,7). The magnetic field is model (magnetostatics) is formulated in the magnetic scalar potential. Its solution provides for the magnetic flux density, magnetic forces in the air gap, and radial magnetic load on the rotor. Displacement of the rotor in axial direction (Oz) with a 0.5 mm step is used to determine the radial forces occurring in the bearing air gap. The analysis of the effects of the changes in the radial load is of a main concern in the simulation PMB because in dynamic conditions, which are due to shifts in the radial work, the knowledge of the magnetic forces provide useful information about the unstable state that may occur in self operation and self-centered that is one of advantages of this type of bearing. This study presents for the first the analysis of the effects of the displacement in the axial direction for PMBs. This result suggests that large and small vibrations appearing in the system model of the permanent magnet bearing will be self-centered.