The circular-arch flexible structure is widely used in various fields, especially the support structure of the optical mirrors. This paper aims to present a generalized formulation of the circular-arch flexible structure and a continuous method to optimize this flexible structure considering the material selection and geometry simultaneously. First, an analytical model based on the variational principle is derived for calculating the radial and tangential stiffness of the flexible element, and then the generalized formulation of the integral flexible structure is obtained by considering force equilibrium and compatible deformation. Second, the structural optimization is implemented by combining the material selection and geometrical parameters, where the continuous artificial variables are used to represent the selected material. Finally, the experimental and numerical examples are given to verify the analytical formulation and the optimization scheme. The experimental and FE simulation results of the flexible element and the integral flexible structure indicate that the presented mechanical model is capable of capturing the linear behavior. For the geometrical nonlinear deformation, there exist some errors. And the optimization results demonstrate that the presented scheme is able to obtain the discrete material design and the optimal geometry.