Abstarct: In this thesis, the nonlinear vibrations of a rectangular hyperelastic membrane resting on nonlinear Winkler-Pasternak elastic foundation subjected to uniformly distributed external pressure is investigated. The membrane is composed of an incompressible, homogeneous and isotropic material. The elastic foundation includes two Winkler and Pasternak linear terms and a Winkler term with cubic nonlinearity. Using the theory of thin hyperelastic membrane assuming the finite deformations and Hamilton’s principle, the governing equations are obtained. Also, according to the strain energy function for neo-Hookean hyperelastic constitutive law, the kinetic energy, the work of uniform distributed force and pressure and the effects of damping are determined. By applying Galerkin’s method and considering the transverse displacement in one and two modes, the nonlinear partial differential equation of motion in the transversal direction is transformed to the ordinary differential equations. Then, utilizing the method of multiple scales, the primary and secondary resonances for the oscillations in one and two modes are analyzed. Finally, the effect of the various parameters such as the stretching ratios, excitation amplitude, damping ratio, stiffness parameters of the elastic foundation, and also the detuning parameter on the vibration behavior of a rectangular hyperelastic membrane is investigated