The use of wear-free, frictionless clearance seals in linearly driven miniature cryocoolers has tremendously increased the reliability and life of such units as compared to those using contact type seals. This has been achieved by employing a non-conventional suspension system, called Flexural Suspension or Flexure Bearing. The earliest Oxford Cryocoolers utilized flexure elements with three spiral arms, which is called as spiral arm flexure bearing. In general, the flexure bearing has a threefold design requirements, viz. fatigue strength, radial stiffness and axial stiffness. In this paper, finite element analysis (FEA) of flexure bearing is carried out. A finite element model of spiral arm flexure bearing is obtained by using CATIA and Hypermesh software. This model is analyzed for stress and fatigue life by using MSC Nastran and MSC Patran software with Durability module. The effect of thickness and material variation is analyzed for stress and fatigue life of spiral arm flexure bearing.