In the present work, the vibration problems of rectangular plates modeled by Eringen's microstretch theory are investigated for the identification of the upper bounds of the microstretch moduli of the plate material. The calculated frequencies of the plates are obtained by extending the Ritz method to the microstretch plates. The three dimensional (3D) vibration analysis of the plates shows that some additional frequencies occur among the classical frequencies as characterizing the microstretch effects. Then it is also observed that these additional frequencies disappear and only the classical frequencies remain with the increasing values of microstretch constants. The inverse problem is established for the identification of the upper bounds of the microstretch elastic constants as an optimization problem where an error function is minimized. (C) 2008 Elsevier Ltd. All rights reserved.