Abstract: Numerical simulation method for the dynamic response of transverse vibration of shaft systems in hydro generators is studied. Gyroscopic effect and bearing coefficient non linearity of the shaft system are considered. Time discontinuous finite element method based on the Galerkin format is used. Method of calculation based on time discontinuous finite element method for the dynamic response of transverse vibration of shaft systems in hydro generators is presented. In the light of this method a computational program is developed and consequently applied on a representative hydro generator as an example. The method given in this paper is thus verified and validated, and can be used for response simulation of rotor systems with non linearity problems.