In mixed finite element formulation three different methods: (1) Hellinger-Reissner principle (HR); (2) Hu-Washizu principle (HW); (3) Gateaux Differential Method (GDM), are widely used. In this study using the GDM, a functional and a plate element capable of modeling the Kirchhoff type orthotropic plate resting on Winkler/Pasternak (isotropic/orthotropic) elastic foundation are given and numerical results of a free vibration analysis is performed. The GDM is successfully applied to various structural problems such as space bars, plates, shells by Omurtag and Akoz. The PLTEOR4 element has four nodes with 4 x 4 DOF. Natural angular frequency results of the orthotropic plate are justified by the analytical expressions present in the literature and some new problems for orthotropic plate on elastic foundation (Winkler and Pasternak type foundation) are solved. Pasternak foundation, as a special case, converges to Winkler type foundation if shear layer is neglected. Results are quite satisfactory. (C) 1998 Elsevier Science Ltd. All rights reserved.