Abstract: A transfer matrix impedance coupling method for eigensolutions in rotor-dynamics is developed. The concepts of substructure synthesis and coupling of mechanical impedance data are applied to this method,so that the application of the traditional transfer matrix method can be extended to the dynamic analysisof complex rotor-support sysems. For the systems with only one interconnection, such as single rotor with one flexible support, the eigenvalues can be readily obtained without any iteration form intersections of the critical speed map of rotor subsystem and the mechanical impedance curve of flexible support one. The present method can be used for eigensolution of the complex multi-spool rotor system with intershaft bearings and special shape of rotor structure, no matter whether it has isotropic or orthotopic properties, as well as it is undamped or damped,The analysis can be completed by calculation only or in combination with test data. Numerical examples show that this method is suitable for engi-neering application with high accuracy, convenience and low cost.