Flexure spring suspensions have demonstrated the ability to provide long operating lifetimes for cryocoolers. The good flexure spring need high radial stiffness and high fatigue life. The profile curves are very important for flexure spring. In this paper, based on the finite element analysis software (ANSYS), geometrically nonlinear static structural analysis and nonlinear dynamics structural analysis were made to several different flexure springs. The fatigue strength, axial and radial stiffness, modal frequency were calculated and listed. The different performance between linear flexure spring and spiral flexure spring were discussed, which would provide an advisory opinion for the design and application of flexure spring in space cryocooler.