The torsional stiffness of gear pair transmission chain usually employed in rotary table plays an important role in both static and dynamic characteristics of machine tools. Taking the gear pair transmission chain as study object,considering the mesh stiffness of gear pair & torsional stiffness of shaft,a general mathematical model for torsional stiffness of gear pair transmission chain is established. Meanwhile,taking a two-stage transmission as example,the effectiveness of analytical model is verified by using the finite element software. Furthermore,the mathematical model for optimal design of transmission chain is constructed,a lightweight design of the transmission chain is carried out by considering the torsional stiffness constraint. The optimization results show that the volume is obviously smaller after optimizing under the premise that the torsional stiffness of transmission chain is guaranteed.