The Stone Age, the Bronze Age, the Iron Age ... Every global epoch in the history of the mankind is characterized by materials used in it. In 2004 a new era in the material science was opened: the era of graphene or, more generally, of two-dimensional materials. Graphene is the one-atom thin layer of sp 2-bonded carbon atoms arranged in a honey-comb lattice. It possesses the unique physical properties: graphene is the strongest and the most stretchable known material, has the record thermal conductivity and the very high intrinsic mobility and is completely impermeable. The charge carriers in graphene are the massless Dirac fermions and its unique electronic structure leads to a number of interesting physical eff ects, such as the minimal electrical conductivity, anomalous quantum Hall effect, Klein tunneling, the universal optical conductivity and the strong nonlinear electromagnetic response. Graphene offers and promises a lot of different applications, including conductive ink, terahertz transistors, ultrafast photodetectors, bendable touch screens, strain tensors and many other. In many applications, graphene (single or multi layered) is used within a polymer matrix in composites form. In this research, an ideal graphene with hexagonal bonds between its atoms, located in the polymer matrix, under biaxial external pressure and thermal loadings is investigated. The composite is single layer and different boundary conditions including clamped and simply supported are considered. For modeling of the problem, firstly displacements are estimated using the third order shear deformation theory and Winkler and Pasternak models are used to model polymer matrix. Then, dynamic equilibrium equations are obtained using the Strain-Inertia Gradient theory and solved using Generalized Differential Quadrature (GDQ) method. The temperature distribution is assumed to be linearly distributed in terms of the length and width of the structure. Natural frequencies and corresponding mode shapes which are depending on the system parameters are calculated at different temperatures, and the effect of parameters such as coefficients of Winkler and Pasternak, Strain-Inertia Gradient parameters and the number of lattice points, are obtained. The high hardness of the system is resulted from very high natural frequencies obtained in this study. Keywords: Graphene, Nanoplate vibration, Generalized differential quadrature, Third order shear deformation