Modal differential sub-structure that can quickly predict effects of structural modifications has been proposed by the author. This method is a kind of the component modal synthesis and utilizes modal analysis results of the model before the structural modification. Because the method does not require the user to decide the component to be modified beforehand, the user can determine the component to be modified after checking the calculation result of the full structure. This method can be applied to free structural modifications such as substitution of a structural part. In a certain case, however, where the model has to handle very many modes, the eigenvalue problem becomes insoluble due to singularity of the mass matrix. This paper elucidates the reason of the problem and shows a procedure to avoid it.