As spectral resolution increases, the dimension of the Doppler Asymmetric Spatial Heterodyne (DASH) interferometer increases. The existing approach for stably mounting the interferometer is limited to mounting a normal-sized DASH interferometer. In this study, a novel and stable structure is proposed, with its effecti1veness exemplified for a near-infrared (NIR) DASH interferometer. The mathematical model of a flexible structure was established. The parameters of the support structure were optimized by requiring the mechanical stress of the flexible structure and shear stress at the bonding surface to be less than the strength value. The spring constants were optimally designed to adjust natural frequency and minimize stress. The finite element analysis (FEA) results show that the maximum mechanical stress was 65.56 MPa. The maximum shear stress was 3.4 MPa. All stress values had a high safety margin. The mechanical material and adhesive area were optimally designed. Therefore, the thermal resistance of the structure was improved by 7.5 times. The test results indicate that the proposed flexible support structure could satisfy the requirements of the launch environment. The results from FEA and vibration tests were consistent with the model calculation results. Compared to existing structures, the mechanical performance and thermal resistance were improved.