In the present work, damaged plates are modeled by the micro-elongation theory which neglects the micropolar effects in Eringen's microstretch theory. The wave propagation problem is Studied and a new wave which does not appear in the classical theory of elasticity is observed. The Ritz method is extended to the microelongation theory and triplicate Chebyshev series multiplied by a boundary function are used as admissible functions to approximate plate deflection, and the frequency equations of the microelongated plate are obtained by using Chebyshev-Ritz method. The additional frequencies due to the microstructure of the plate are observed among the values of the classical frequencies. We examined the relation between these additional frequencies and the material constants of the microelongated medium and observed that these additional frequencies disappear while the all microelongational constants are taken as zero.