<p>This paper extends the one-dimensional (1D) nonlocal strain gradient integral model (NStraGIM) to the two-dimensional (2D) Kirchhoff axisymmetric nanoplates, based on nonlocal strain gradient integral relations formulated along both the radial and circumferential directions. By transforming the proposed integral constitutive equations into the equivalent differential forms, complemented by the corresponding constitutive boundary conditions (CBCs), a well-posed mathematical formulation is established for analyzing the axisymmetric bending and buckling of annular/circular functionally graded (FG) sandwich nanoplates. The boundary conditions at the inner edge of a solid nanoplate are derived by L’Hôspital’s rule. The numerical solution is obtained by the generalized differential quadrature method (GDQM). The accuracy of the proposed model is validated through comparison with the data from the existing literature. A parameter study is conducted to demonstrate the effects of FG sandwich parameters, size parameters, and nonlocal gradient parameters.</p>