Abstract : In the range of milliwatt to a few watts cooling capacity, Stirling cycle and pulse tube coolers are most suitable for producing cryogenic temperatures owing to their eco-friendliness, high efficiency, cooling capacity to mass ratio etc. The compressor of a Stirling cooler is powered by a linear motor. The power piston of the cooler is held in position and moves to and fro with the support of so called flexure springs or flexure bearings. Flexures avoid direct contact between moving parts of the compressor of the cooler. Thus, if designed adequately to withstand fatigue, flexure bearings can easily outlast rolling element bearings and slider bearings. In this work, a computational analysis is used to study the performance of flexure spring by varying the geometrical parameters. Three of the most common spring materials namely, SS304, beryllium copper and spring steel are considered for analysis. The analysis was made by varying the parameters like spiral sweep angle, slot width, number of spirals and disc thickness. The influence of each of these parameters on the fatigue life of the spring has been investigated. The results suggest that flexure springs of three spiral arms would be the ideal choice for the selected cryocooler. The variation of stress developed with respect to different design parameters and fatigue damage factor are presented graphically. © School of Engineering, Taylor’s University.