A mechanical and a parameter optimization model for flexure support structure of optical components were proposed to allow the flexure structure meet simultaneously the requirements of the stiffness for optical component position and the compliance for temperature adaptability。Meanwhile, the corresponding modeling method was investigated. As this flexure structure was consisted of several identical flexure parts, it was simplified into an indeterminate beam structure, and the radical stiffness and tangential stiffness were derived using the virtual work principle. Then, by assuming optical components for the rigid body, the whole stiffness of the flexure support structure was derived based on the force equilibrium and its compatible deformation, and the correction factor was introduced to compensate the error caused by the rigid assumption. Finally, the total strain energy of the flexure structure was taken as the objective function, and the collaborative optimization model was derived considering the geometrical pattern and parameters simultaneously. By introducing the integral variables, the whole stiffness of the structure was simplified into a linear combination of the integral variable and discrete stiffness, and the harmonic terms were eliminated. The whole stiffness model was verified by the simulation and experiment, and the experiment results are highly in agreement with the simulation results. A lens mounting was taken for an example, the optimization method of the flexure mounting structure was verified. The finite element simulation results show that the surface precision of the lens has been improved by 23%.