The vibration of a flexible shaft coupled with multiple flexible disks is investigated by using a substructure synthesis technique with the assumed modes method to be compared with experimental results. According to the nature of coupling with the rotor, disk vibratory modes are classified into three groups: uncoupled disk modes with more than one nodal diameters, umbrella modes coupled with the shaft longitudinal vibrations and disk modes with a single nodal diameter coupled with the shaft bending vibrations. The natural frequencies and mode shapes for each group are calculated by employing different solution and tuning techniques. It is shown that the tuning technique is capable of accurately predicting the natural frequencies of the complicated coupled vibratory system. (C) 1997 Academic Press Limited.