Abstract: To satisfy the requirement of thermal adaptability and limited space, a kind of bipod flexure mounts for space reflector (Ø355mm) made of super low expansion coefficient glass was designed by finite element analysis (FEA) method. Firstly, the basic design principles of bipod flexure were studied. The advantage of bipod structure, compared with three points backside structure, was discussed from the view of freedom. Secondly, simulation analysis and optimization design were carried out for the influence of dimension parameters of support structure and flexure hinge on the surface figure accuracy. The intersection position of supporting foot extension line should be the key design parameters and the bonding position should be designed respectively. The results indicate that backside bipod flexure mounts after improved design has fine thermal adaptability and can effectively discharge the load caused by thermal variation, and has fine supporting ability and dynamic stiffness at the same time. root mean square of surface figure accuracy reaches 3.68nm, after reflection mirror mounting, and the first order frequency of assembly is 123.41Hz. The data can meet the design requirements. This study can supply the meaningful reference for future structure design of backside bipod mounts.