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In the following research, the buckling of multilayered CNT/GPL/Fibre/Polymer hybrid composite Levy-type nanoplates resting on Winkler–Pasternak support is investigated using modified nonlocal first-order plate theory. The different layers of the plate are assumed to be reinforced with functionally graded carbon nanotube composite or functionally graded graphene platelets composite. Modified nonlocal first-order plate theory is used to capture the molecular effects at nanoscale and extract the buckling equations. The along-thickness variation of reinforcing nanocomposites may be uniform or functionally graded, and functionality can be linear or nonlinear based on specific functions presented by scientists. Using a closed-form analytical solution, these partial differential governing equations are changed to a set of coupled ordinary differential equations that may be solved for the Levy-type boundary conditions (i.e., two opposite edges with simply supported and two other with edges arbitrary). The obtained results may be used as a useful benchmark for validation of other works developed in the future. [ABSTRACT FROM AUTHOR]