In order to ensure the position accuracy and the stiffness of the support system for the 4 m SiC primary mirror, the parameters of hardpoints in a hexapod configuration were analyzed according to the optical indexes of the primary mirror support system. Using the finite element method, the hardpoint positioning mechanism was optimized. The hardpoint distribution radius, positioning angle, axial stiffness and the limit of axial tension and compression were determined by the finite element software. The analysis results show that six hardpoints should be equally distributed at 1 345 mm of the radius on the circumference in the primary mirror backface. When the axial stiffness of the hardpoint reaches 15 000 N/mm, the natural frequency of the primary mirror support system is greater than or equal to 15 Hz. It can meet the design requirements and provide the basis for the following design optimization.