The transfer matrix of a flexure hinge was derived on the basis of balance equations and the virtual work principle with consideration of axial, shear, and bending deformations. The element stiffness matrix of a flexure hinge was obtained from the relationship between the transfer and stiffness matrices. In this manner, the unified formula of element stiffness of a general flexure hinge was established. By using this method, rigidity models of parabolic, corner-filled, and the right circular flexure hinge have been deduced. By taking the right circular flexure hinge as an example, the result obtained using this method were compared with those of methods provided in other studies and the finite element results. The comparison results revealed that the proposed method increases the rigidity accuracy because the effect of the uneven distribution coefficient of shear stress was considered. The stiffness error was within 10%, which demonstrates the validity of this method. In contrast to the other methods, the proposed method can be applied by determining the first integral element stiffness of a common flexible hinge. Moreover, the proposed method provides better commonality, flexibility, and ease of programming. In particular, it is much easier for the flexure hinges with a complex contour curve. Transitivity can be used to calculate the rigidity after the flexure hinge has been divided into subunits, thus making it unnecessary to convert to the global coordinate system.