Stiffness is an important parameter index affecting the mechanical performance of flexible hinges. The tensile stiffness model of a composite flexible hinge was established. The analytical solutions were calculated under different parameters and different sizes. The static simulation was carried out by using ANSYS Workbench. The influence of the various structural parameters on its stiffness was analyzed. It is concluded that the composite flexible hinge has a larger output displacement than the traditional double parallel hinge under the same size and force. Under the condition that the errors between the analytical solutions and the simulation results were small, the flexible hinge with optimized parameters was designed and a measuring platform was built to measure the straightness of the guide screw driven by the ball screw. The measured results were compared with the results from the laser interferometer. It is shown that the measurement platform based on flexible hinges meets the requirements.