The aim of the work was modelling of shaft and calculation of natural vibration frequencies and critical rotations of a large-size, vertical mixed flow pump of total length l=4866 mm. Equations of motion were determined analytically, and then calculation results were verified by numerical modelling. The difficulty of the problem consisted in the shaft bearing, in which four hydrodynamic bearings of unknown parameters were applied. A four-mass beam supported on flexible supports of rigidity k and damping c was assumed as the discrete model of the shaft. Equations of motion for the system were derived with the method of forces. In order to verify correctness of the derived equations, one considered three models of the beam with different support configuration: the beam supported on rigid supports, the beam supported on elastic supports, and the beam supported on flexible supports of rigidity k and damping c. Calculation results are presented in tables and graphs.