Aiming at the bearing capacity of TBM hydraulic propulsion mechanism under the conditions of large sudden load and extreme heavy load, the stiffness performance performance and sensitivity of TBM hydraulic propulsion mechanism are studied. The method regards the cylinder block, piston and hydraulic oil of each hydraulic propulsion cylinder branch chain connected in parallel as a multi-flexible body connected in series. The static stiffness model of the propulsion cylinder is established and its effectiveness is verified by the finite element method. Then, the mechanism kinematics model was established using the principle of differential motion of the parallel mechanism, the deformation coordination equation and the dynamic compatibility equation were established, and the relationship equation of the static stiffness of the mechanism was obtained, and its effectiveness was verified by the finite element method. The relationship between the stiffness of the mechanism and the structure size and pose was obtained with the sensitivity analysis method. The results show that the wedge angle of the mechanism and the size of the movable platform have a greater influence on the stiffness of the transverse x-axis, vertical y-axis and the longitudinal z-axis rotation stiffness. The lateral x-axis stiffness, the vertical y-axis stiffness and the steering stiffness are equal respectively, the distribution law of the stiffness deviation in all directions of the mechanism is the same and gradually decreases with the increase of the longitudinal displacement, the calculation deviation does not exceed 2%.