To improve the dynamic performance of a radial driving shaft employed on an aero engine,a theoretical analysis based on FEM is conducted. Dynamic model and equation is constructed consistent with the actual structure and practical operating condition. The influences of gyroscopic moment,supporting stiffness and location of the intermediate fulcrum on shaft critical speed are discussed. The method to determine the intermediate supporting location is suggested,which is believed to be valuable in practical design of radial driving shaft. Analysis results indicate that the gyroscopic moment has minimum impact on the natural frequency,less than 0.5%. When the intermediate fulcrum is located at the point of the ‘ Natural Mode' of second curved modal shape with no intermediate fulcrum,the highest critical speed and design margin of supporting stiffness could be achieved. The experimental results prove the correct of the theoretical analysis.