| With the development of exploration of the universe, the larger apertures of telescope are needed. Thirty Meter Telescope (TMT) represents the manufacturing forefront of large telescope. The surface figure error of the mirror is a key factor which affects the imaging quality of telescope. The support structures of the tertiary mirror are designed, which should meet the required surface accuracy.On the basis of lots of references, the development and current situation of the large ground-based telescope are reviewed. The fundamental of mirror support is studied and the different types of axial and lateral supports are summarized. Basic principles of FEM are elaborated and summarized.According to the feature of TMT tertiary mirror,2-level18-point whiffle tree structure is used in the axial support. The best locations of the support points are found with Ansys. The support structure is designed and the FEM model is established with MSC.Patran/Nastran. Based on the result with FEM analysis, the support structure is modified. So the influence that the asymmetry of structure causes the asymmetry of deformation of the mirror surface is eliminated. The RMS of the mirror surface deformation is99.7nm, which meets the design requirements. On the other hand, a kind of semi-active axial support is designed and it also conforms to the requirements of the mirror surface accuracy.To the solid plane mirror like TMT tertiary mirror, the numbers and locations of the lateral support points have little effects in mirror surface accuracy. It affects only the edge of the mirror. Learn from the experience of axial support,12-point whiffle tree structure is used in the lateral support. With the FEM analysis and changes, the RMS of the mirror surface deformation is14.1nm with the lateral support alone. In the end of the paper, under the combined effects of the axial and lateral supports, the result meets the requirements of the mirror surface accuracy. |