Abstract: In this paper the validity of the cross modal synthesis model for modal analysis of multi-arch dams proposed by the author is demonstrated. It is demonstrated firstly that the linear space consisting of the submodal vectors of the substructures is complete. As the number of truncated submodal vectors of the substructures is increased to the full number, the calculation result will be equal to that of the global calculation. So it is also demonstrated that the approximation calculation will approach to the valid result .