The natural frequencies and modes of the longitudinal coupled vibrations in a flexible shaft with multiple flexible disks are determined through a substructure synthesis technique. The analysis rotor model consists of multiple flexible disks attached to a flexible shaft with varying annular cross-section, as used for steam turbines or computer storage devices. In modelling the system, disk flexibility and centrifugal stiffening effects are taken into account. Commercial computer hard disk drive spindle systems are selected as illustrative examples. In particular, the effects of disk flexibility on the longitudinal coupled vibrations between the shaft and disks are investigated with varying spindle rotational speed. The results indicate that the substructure synthesis technique allows a clear physical insight into the effect of disk flexibility with reasonable computational effort. (C) 1997 Academic Press Limited.