In this paper, the wave propagation method is combined with nonlocal elasticity theory to analyze the buckling and free vibration of rectangular Reddy nanoplate. Wave propagation is one of the powerful methods for analyzing the vibration and buckling of structures. It is assumed that the plate has two opposite edges simply supported while the other two edges may be simply supported or clamped. It is the first time that the wave propagation method is used for thick nanoplates. In this study, firstly the matrices of propagation and reflection are derived. Then, these matrices are combined to provide an exact method for obtaining the natural frequencies and critical buckling loads which can be useful for future studies. It is observed that obtained results of the wave propagation method are in good agreement with the obtained values by literature. At the end the obtained results are presented to evaluate the influence of different parameters such as nonlocal parameter, aspect ratio and thickness to length ratio of nanoplate.