Heavy duty deflection angle milling head is the core functional unit of heavy-duty gantry CNC machine tools. Stiffness of swing chain system is one of the important factors that determines accuracy of heavy duty deflection angle milling head. In order to improve dynamic performance and mechanical precision, the gear pair and support system of the swing chain are studied in the paper. Based on the deformation compatibility condition and the superposition theorem, the torsional deformation and stiffness of each part are analyzed, and considered the deformation of workpieces and supporting system and the interaction of them. The vulnerable segment is found out in the paper, which is valuable to amend and improve the design of milling head. At last, the curves of the relation between the swing chain stiffness and the gear parameters and bearing preload are charted, which provide the theory and technical support for digital design, optimization of the milling head and the basis for the similar driving system stiffness calculation.