In the applications of linear compressors, flexure bearings maintain axial periodic motion of the piston without offset in the radial direction. This is very important for the seal clearance of the compressor. The performance of different thicknesses, number of slices, spacings, and spatial arrangements of flexure of the bearing component were compared on the basis of finite element analyses. The performance of radial stiffness and the torque characteristic has been especially considered. The conclusions drawn from this study can be used to guide the design of a flexure bearing component.