Non-linear free vibration of hinged orthotropic circular plates with a concentric rigid mass at the centre is studied by using the finite element method. Hamilton's principle is applied to derive the basis non-linear partial differential equations and associated boundary conditions for the problem of large amplitude of an orthotropic circular plate. The applications of the finite element method to the dynamic problem rely on the use of a variation principle to derive the necessary element property's equations. The assembled equations for the plate are formed by summing each of the element equations obtained in consideration of a single element. Then, the boundary conditions are imposed on the vector of nodal field variables, so that the appropriate boundary conditions are satisfied. The assembled equations form an eigenvalue problem and are solved for the unknown field variables. The relations between the fundamental frequencies and the amplitudes of non-linear vibrations of the circular orthotropic elastic plate with a rigid core are obtained. The results show that the frequency responses of the plate varies with changes of boundary conditions and the ratio between tangential and radial elastic constant.