Abstract: The finite element, method is used to analyze dynamic problems of rotor-bearing systems. The system motion equations are presented in a fixed and a rotating coordinate systems. Nelson's element is extended to considering transverse shear effects, which are of great importance for complicated aircraft engines.A program （FEPRS） is presented for dynamic modelling of the rotor-bearing system which consists of rigid disks, distributed parameter finite rotor elements and discrete bearings. The whirl frequencies can be calculated for complicated rotor-bearing systems in various whirl states, and mode shapes can be automatically drawn by implementing this program on a computer. A lot of practical examples have been analyzed. The results are satisfactory in comparison with experimental data.