This paper aims at three typical flexure hinges, and analyzes the nonlinearity of the flexure hinges. Because hinges need linear deformation, using the finite element software ANSYS to study the performance of the hinges, then discusses the hinges parameters' impact on linearity. Because flexure hinges use metal material, which can only produce minor deformation. When the acting force is too big, the flexure hinges may bow, so this paper analyses the structure nonlinearity of flexure hinges which under the maximal acting force, and calculates the hinges linearity efficient range, all of the above provide a certain rationale to the application of flexure hinges in mechanisms.