Abstract: Theoretical aspects of a new capability to determine the coupling vibration of turbomachines subjected to shrouded blades and disc assemblies are presented. Turbosystems such as advanced turbo-fan aeroengines with shrouded fan blades and disc coupling systems which have freely slipping shroud contact surfaces can be investigated using this capability. By means of fixed interface modal synthesis technique combined with penalty function, the coupling vibration characteristics of the quasi-periodically symmetric assemblies are analyzed. The developed numerical method by using finite element analysis and the corresponding software system are both accomplished. The scale of calculation can be reduced remarkably under the pre-condition of ensured sufficient accuracy of dynamic analysis. Therefore, the obviously economic benefits are emerged. It already has been analyzed and the practical conclusions can be effectively applied for academic and industrial fields.