Abstract: In accordance with the relationship between the eigen-matrix rank and sub-eigenfunctiondimension of eigen-values, the maximum number of possible multiple roots for anti-plane problemand in-plane problem is determined. In view of the relationship with eigen-values of anti-plane andin--plane problem, the eigen-values for Reissuer plate consists of two parts. One part associateswith anti-plane problem, the other part pertains to in--plane problem. Therefore, the maximumnumber of multiple roots for anti--plane ...