With the widely development of nanotechnology in a lot of branches of life and technology, nanoplates like another nanostructure have been used in a lot of applications and because of this reason it was very important for researchers to study this type of nano structures and achieve development at this type of research. The characteristic and analytic of forced vibration of simply supported nanoplates is studied using the classical laminated plate theory and nonlocal elasticity theory by taking into account the effect of viscoelastic foundation. This type of foundation is modeled as Kelvin-Voigt foundation and the material properties of the nanoplate are assumed to be orthotropic. Equation of motion is derived and Navier method as an efficient and accurate analytical tool is used to solve the forced vibration equation of motion for the simply supported ends. The parametric study shows that damping of foundation, damping of the nanoplate, nonlocal parameter, stiffness, aspect ratio, excitation frequency and position of the load have significant effects on the dynamic response of the nanoplate. The results showed that deflection of the single layer graphene sheets decreases by increasing damping of the surrounding medium, structural damping of the nanoplates and nonlocal parameter. Deflection decreases by increasing the aspect ratio of the nanoplates until specific value. Nanoplate deflection is influenced by excitation frequency of the external load at small values of nonlocal parameter. For elastic nanoplates, there are two resonance peaks for the deflection which accommodate the first two natural frequencies of the nanoplate.