To increase the anti-torsion stiffness of secondary mirror support structure of a telescope and to reduces the obscuration from the support structure, an imposed preload of 8-vane spider was designed to replace the original 4-vane spider. According to the Euler-Bernoulli beam theory, the mirror support structure was simplified as a simple model consisting of a beam and a mass point, and then the simplified model was divided into two more simple kinetic models. By selecting the appropriate mode function, the numerical solution of the first order modal for the simplified model was deduced with Rayleigh and Dunkerley approaches. Obtained calculated results are in good agreement with that from Fnite Element Analysis (FEA). Moreover, in order to solve the impact of the preload on this structure, a coefficient was deduced in theory. Then, the model was simulated by FEM and the result obtained in FEM is the same as that calculatedone one in theory. The analysis results prove that the method is available for the calculation of the similar structural dynamics characteristics. The simulations show that the first order modal of the structure can change from 11.6 Hz to 23 Hz when the preload increases up to 20 kN, which proves that the preload can effectively impact on the anti-torsion stiffness and reduce the secondary mirror support weight and obscuration ratio. The results can give a reference for designing secondary mirror support structures.