The present study proposes an analytical solution for the axisymmetric/asymmetric buckling analysis of thin circular/annular nanoplates under uniform radial compressive in-plane load. In order to consider small scale effects, nonlocal elasticity theory of Eringen is employed. To ensure the efficiency and stability of the present methodology, the results are compared with other presented in literature. Material properties including Young’s modulus, density, Poison’s ratio are assumed to be constant through the body of nanoplate. In addition, the effect of small scales on critical buckling loads for different parameters such as radius of the FG nanoplate, boundary condition, mode number and geometry parameters are investigated. In order to obtain the critical buckling load, the asymmetric modes as well as axisymmetric modes are considered. The thin nanoplate is modeled using Kirchhoff plate theory.