The calculation model by applying mode synthesis method for lateral (bending)-torsional coupled vibration of two-shaft geared motor-driven rotor system is proposed in this study. Mode synthesis method, which enables to greatly reduce degrees of freedom without increasing calculation errors, is essential for such time and memory consuming vibration calculation. This calculation model deals with stiffness and non-proportional damping for bearings or seals for lateral directions as inner elements comprising inner systems, whereas stiffness of gear tooth contact for its normal direction is handled as a boundary element as provision for further extension to more complicated tooth contact model. The reduced calculations of eigenvalues, frequency response analysis and transient excitation analysis for coupled lateral-torsional vibration were performed. The results show that reduced model properly inherits selected vibration modes from original DOF model.