Within the framework of a variational mixed formation and higher-order shear deformation theory (HSDT), a numerical approach is developed in this research to investigate the buckling and post buckling behaviors of variously-shaped plates made of functionally graded graphene platelet-reinforced composites (FG-GPLRCs) taking the effect of porosity into account. By the proposed approach, which can be named as VDQ-FEM, thick and moderately thick plate-type structures with different shapes (e.g. rectangular, skew, or quadrilateral) with arbitrary-shaped cutout (e.g. circular or rectangular) can be studied. Various types for porosity distribution scheme and GPL dispersion pattern including uniform and different functionally graded patterns are considered along the thickness of plate. In the computation of material properties, the closed-cell Gaussian Random field scheme and Halpin–Tsai micromechanical model are utilized. One of the key novelties of proposed approach is developing an efficient way according to the mixed formulation to accommodate the continuity of first-order derivatives on the common boundaries of elements for the used HSDT model. Several numerical examples are given to analyze the influences of porosity coefficient/distribution pattern, GPL weight fraction/dispersion pattern, cutout and boundary conditions on the buckling and postbuckling characteristics of FG-GPLR porous composite plates.