Taking the multi-span rotor system composed of two double diaphragm couplings coupled with three rotors as the object, the finite element model of the high-speed multi-span rotor system is established, and the critical speed of the rotor system is solved using ANSYS Workbench software. The effects of the radial stiffness of the diaphragm coupling and the bearing support stiffness on the critical speed of the rotor system in the first three orders are analyzed. The results show that, for the model established in this paper, within a certain range, the radial stiffness of the diaphragm coupling has a greater influence on the third-order critical speed of the multi-span rotor system, and the increase of the radial stiffness of the diaphragm coupling and the increase of the bearing support stiffness will increase the critical speed of the multi-span rotor system.