Abstract: Based on finite element simulation， the influence of the structural parameters of the spiral flexure spring on its stress distribution and stiffness is studied. For the gap seal design of flexure spring of mechanical refrigerator， it points out the variation law of radial stiffness under different radial force angles and eccentricity. The stiffness of the Archimedes spiral is theoretically analyzed， and the axial stiffness formula is obtained. The stiffness-stress coefficient is proposed to evaluate the spring performance. Finally， the theory is applied to the finite element simulation. Under the same axial stiffness， the maximum stress of the Archimedes spiral is the smallest compared with the other four spiral profiles， which is beneficial to the spiral profile flexure spring design of the long-life mechanical refrigerator.