Abstarct: These days, nanostructured materials such as nanobeams and nanoplates have many applications in industry and research. One of the most widely used nanostructured materials is nanoplate, which are used in exchanger, sensors and multi function devices. Usually, the dynamic deformation of these materials is important, so the dynamic and vibration behaviors of nanoplates have been studied by researchers. Therefore, in this work, the nonlinear vibration analysis of a double-nanoplates coupled by a nonlinear elastic medium is investigated. The system is subjected to external harmonic excitation. Nonlocal elasticity theory is used to obtain the nonlinear governing equations of motion. The Galerkin method is used to discretize the nonlinear governing equations into the ordinary nonlinear differential equation. After discretizing of the nonlinear governing equations, the multiple scale method is used to solve the nonlinear differential equation. Finally, the effect of various parameters such as elastic medium, nonlocal parameter and other geometric and structural parameters on the nonlinear vibration of the system is studied.