To meet the requirements of the Tertiary Mirror System (M3S) in a Thirty Meter Telescope(TMT) for mass and stiffness, how to allocate rationally the stiffness for different parts in the system was researched. As the first-order resonant frequency of M3S should not be less than 15 Hz, the composition of M3S was researched, then a four-point lumped-mass model was established by the pre-designed data. Furthermore, the stiffness of the mirror support system was calculated, and an eigenvalue inverse solution was used to obtain the stiffness matrix of a simplified model in six global directions. Finally, stiffness of all springs in the system was given, and the simplified model and the calculated results were used to guide the structure design and control design later. The simulation software Adams was used to verify the stiffness allocation and analysis process. The results show that the stiffness allocation of the M3S is reasonable and the first modal frequency of the system can achieve to 15.2 Hz, which meets the design requirements. With the stiffness allocation, the system design can offer higher efficiency and rationality.