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During the processing of an optical mirror, the performance parameters of the bottom support system would affect the surface forming accuracy of the mirror. The traditional bottom support system has a large unadjustable support stiffness, which increases the difficulty of unloading the impact force generated by the grinding disc. In response to this scenario, a flexible support system (FSS) consisting of 36 support cylinders with beryllium bronze reeds (BBRs) and rolling diaphragms (RDs) as key components is designed. It is necessary to analyze the key components of the support cylinder to reduce its axial movement resistance, ensure a consistent force output of each support point. First, the internal resistance model of a flexible support cylinder is established, and the main factors of internal resistance are then analyzed. Thereafter, the multi-objective structural parameters of the BBR and RD are simulated in ANSYS using the control variable method. The optimal structural parameters of BBR and RD are determined by simulation. Finally, experiments are performed on the RD ultimate pressure, internal resistance of the support cylinder, and consistency of the force output of the FSS. The experimental results show that the support cylinder with the optimized design has good force output consistency, which provides a theoretical basis for the application of FSS in optical mirror processing.