The transfer matrix method of vibration analysis is widely used for the calculation of the natural frequencies of turbo-generator rotors, and of propeller blades, axial compressor blades, turbine blades, and helicopter rotors. A comprehensive account of the method has been given by Pestel and Leckie. The basis of the method is to deine a state vector, which gives all the generalised displacements and forces at a given cross-section of the system. The state vector at one cross-section is then related to the state vector at a neighbouring cross-section by means of a transfer matrix. It is found that, by a suitable choice of the order and signs of the elements of the state vector, the transfer matrix can in many cases be made symmetrical about the secondary diagonal; that is the diagonal running from the top right corner to the bottom left corner of the matrix and is also often called the “cross diagonal”.