The main objective of this research is to investigate the stability analysis of the composite laminated plate-Pastenak-type (two-parameter) foundation interaction and the influence of the second parameter on the critical buckling loads. Two-parameter foundation models are more accurate than the one-parameter (Winkler) foundation model. A functional for thin laminated composite plates is obtained with the proper dynamic and geometric boundary conditions using the Gateaux differential via potential operator concept. The functional is linearized by the incremental formulation, and the necessary steps of the stability analysis for the mixed finite-element method are given. As a special case if the second parameter is neglected, the mechanical modeling of the foundation using the Pasternak formulation converges to the Winkler formulation. A four-noded quadrilateral, isoparametric, C-0 class element with 4 X 9 degrees of freedom is generated. The independent variables per node are three translations, three membrane forces, and three moments. The element is verified by the numerical studies existing in the literature, it is observed that the influence of the second parameter on the critical buckling loads is noticeable, and the results are closely related to the foundation modeling.