In this study, rectangular plates subjected to static loads and supported on a discontinuous two-parameter elastic foundation are analyzed. The formulae for the computations are developed from improved shear deformation theory, where the displacement w is divided into bending and shear strain components. The results obtained from this article and other publications are evaluated to prove the accuracy of the proposed theory and the calculation program. Then, a parameter study is carried out to capture the effect of some material and geometrical parameters on the static response of structures. Especially the influence of the flexoelectric effect and discontinuous foundation is investigated. As two elastic foundation parameters and flexoelectric coefficient are increased, the non-dimensional maximum deflection of the plate decreases, indicating that these factors improve the plate's stiffness.