Abstract: Thirty Meter Telescope's tertiary mirror is an elliptical ceramic glass reflector whose major axis is 3.594 m and minor axis is 2.536 m. Flexure structure was widely used in the mirror's support structure to release all the other degree of freedom except those along the support direction. The design decoupled the axial and lateral support and reduce the thermal stress due to the material mismatch. The higher compliance would benefit the telescope's mirror surface under distortion, but the buckling criteria load would decrease correspondingly, either. So the limit load of each flexure structure should be calculated as the design input. And the buckling safety factor SFBuckling was analyzed for each part under the limit loads. Eigenvalue buckling analysisand nonlinear buckling analysis were both taken and compared. Based on the analysis results, the design were optimized iteratively to achieve balanced values of compliance for all the flexure. The mirror surface error under thermal distortion met the design requirements.