In rotating machinery, unbalance and misalignment are major concerns in vibration. Unbalance can be eliminated by balancing procedure to some degree. but little work has been done on the vibrations that occur in a misaligned rotor system. Currently, no generalized theoretical model based on a rotor system with flexible coupling is available to describe the vibrations caused by misalignment. As a part of systematic investigation on the misalignment, first of all, the study on flexible coupling with misalignment should be preceded. In this study, the geometry and reaction force and moment of a gear coupling with misalignment was investigated, also the theoretical model of a gear coupling with misalignment was presented by using the relationship between geometry and moment of gear coupling. It is expected that the proposed procedure can be applied to derive the theoretical model of other couplings.