Abstract: A flexible support structure was designed to make the mirror surface figure error and the stiffness of the structure fulfill the requirements of the design of a 2m telescope's K mirror. KM1 was the support at three points on the rear of mirror. The position of support points was optimized by the FEA software ANSYS to minimum the mirror surface's RMS. And the flexibility matrix of the flexible support bar was built by theadjoint transformation. Then based on the flexibility matrix, the thickness, length and the width of the flexure hinge were optimized to reduce the thermal stress and assembly stress and fulfill the requirement of the mirror support's stiffness. KM2 was the support at three points which are uniformly spaced around the circum of mirror. The flexible support bar of KM2 was the same as KM1's. The FEA simulation results of KM1 and KM2 under the work condition of gravity and temperature drop met the design requirements. The RMS of KM1 was less than /40, and the RMS of KM2 was less than/60. Their first order resonant frequency was all over 100 Hz.