The critical speeds and responses of uniform, flexible, cylindrical rotors are predicted by use of the Riccati transfer matrix method. The critical speeds are also measured experimentally. The computational and experimental results are in good agreement. The balancing of two cylindrical shell rotors is completed. For the two balanced rotors, no large amplitude vibration occur when the operating, rotational speed passes through critical speeds, and that rotation speed can arrive to a very high value to meet the requirement of isotope separation in engineering.