The plane supporting spring, the radial stiffness of which is considered as one of the most significant parameters in design process and application, is commonly used in the isolation instruments in the fields of aeronautics, astronautics, auto industry, etc. Proposed in this paper is a force-based theoretical method for computing the radial stiffness of multi-spiral supporting spring, which is obtained by solving the component force and radial displacement of each spiral line using the force and energy approaches respectively. Finite element analysis (FEA) of Archimedes spiral-plane supporting springs with 1 to 6 spiral lines is made via speedy modeling by ANSYS parameter design language (APDL). Validity of the theoretical method has been verified by comparison of its calculation results and our numerical analysis. And the relationship between the radial stiffness of plane supporting spring and the key geometrical parameters has been confirmed by our study, which can surely provide insights into the optimal design of plane supporting spring.