Abstract: The characteristics of wave propagation in a periodic plate reinforced byregular orthogonal stiffeners are analyzed using the mutual variational principle. The hi-erarchical finite element method is used to set up the matrix eigen-equation governing thewave propagation problem. The numerical results show that this method can guarantee agood accuracy even in high frequency field.Finally,the effect of the ratio of length to width.the paramaters of the stiffeners and the boyndary conditions are discussed.