An improved transfer matrix method-Whole Transfer Matrix method was applied to calculation of the critical speeds and vibration modes of a dual-rotor system with engine casing.Its potential energy distributions corresponding to each rotor critical speed and vibration mode are calculated and analyzed by this way.Whole Transfer Matrix method takes rotors and cases of the system as a whole body in transferring

the size of the freqency determinant is determined only by the number of rotors and cases

but free from the supports.This method is of great advantage for developing general computer program.The investigation indicated that the vibration level of the rotor system can be found from potential energy distribution.Thus the effective measures can be taken to depress the vibration.