Abstract: Flexible spring，which is used to support the piston components for improving the life and performance of the stirling refrigerator，has played a very crucial role in stirling cooler.Based on the archimedes spiral，a flexible spring was designed for a free piston stirling refrigerator at freezer temperatures.By changing the curve slightly θ，the radius of the element R and the pitch V，the spring provides suitable mechanical stiffness to meet the needs of the stirling refrigerator and reduce its maximum stress to 70%of the fatigue limit.The ANSYS software was used to make finite element analysis of archimedes spiral spring，fermat type spring and sunpower type spring，and the new dimensionless parameter was introduced to evaluate the performance of flexible spring.It was found that the maximum stress of archimedes spiral spring is the smallest and the stability of dynamic radial stiffness is also high.