A laminated composite plate designed is supposed to be used under different end supports. The elastic foundation is one of such conditions. The strength of the laminated composite plates can be enhanced by altering constituents or by the addition of filler materials. For localized strengthening of laminated composite plates, such as at particular layers, it is not cost-effective to strengthen the whole structure. So, the laminated composite plates are strengthened at a particular layer by adding the fillering materials, for example, graphene or flyash. The addition of these filler materials in a particular region sometimes causes agglomeration. Agglomeration of filler materials causes adverse effects such as stress concentration or strain aging. In theoretical formulation, Eringen’s nonlocal principle is applied to account for the impact of agglomeration. In the current study, neat epoxy glass laminated composite plates as well as rectangle laminated composite plate variants with outer layer graphene, core layer graphene, functionally graded laminated composite plate, laminated composite plates exclusively rich in graphene, and laminated composite plates only rich in flyash are taken into consideration. Using a layer-wise model, the fifth-order shear deformation theory is applied. The laminated composite plates are assumed to rest on an elastic foundation. The consequence of elastic coefficient of foundation on procured parameters such as fundamental frequencies, stress parameters, center deflections, and buckling performance is determined. For this purpose, computerized programs are developed using MATLAB and validated first for isotropic material. Further, the work is extended to study these effects on the laminated composite plate variants.