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Recent experience in solving the shaft breakage and seal rub problem of a vertical, eight-stage liquid nitrogen pump at a plant site is documented. Several initial field tests conducted to diagnose the vibration problem are described in detail. The pump is modelled as a dual level rotor bearing system, so account for the vibration characteristics of the support structure and pump casing bundle. A subsynchronous mode associated with the cantilever bending of the pump casing bundle was correctly predicted by this dual level analytical model. This subsynchronous mode would remain undetectable, if the pump were modelled as a single level system with rigid pump casing bundle and inflexible support structure. Also included in the analysis are pertinent representations for throttle bushings, wear rings, bearing bushings, and stator-impeller forces, based on empirical models selected from the open literature. The pump model was calibrated with vibration data of the support structure and the pump shaft. A comprehensive parametric study produced four cost-effective solutions, one of which was chosen for implementation. Subsequent field tests confirmed the reduction of shaft vibrations predicted by the analysis. The pump continues to operate satisfactorily. The combined experimental and analytical approach outlined should be of interest to engineers responsible for solving the vibration problems of vertical multistage pumps.