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In this paper, higher continuity p-version finite element, in particular two-dimensional C2 elements are utilized in studying vibrational characteristics of rectangular Flexural Micro-Plates based on the "gradient elasticity theory". In order to verify the computational procedure, results obtained from the finite element framework are compared to the classical plate theory results and to those of the micro-plate and classical plate investigations that are available in literature. Results indicate that the proposed framework, yields highly accurate results. Moreover, it is concluded that, under certain boundary conditions and length scale effects, the differences in predictions are so gross that the validity of classical theory in predicting micro-plates vibrational characteristics can be ruled out completely.