Environmental issues and energy crisis have caused the world attention to the renewable energies; especially the wind power, since they have low cost and high reliability. To achieve higher capacity, wind turbines have increased in their size over the years. However, the large size of the modern turbines has exacerbated the problem of vibrations, which results in lower efficiency and power generation. Because of the large deformations, the conventional linear theories cannot model the blades accurately, due to the importance of nonlinear effects in large scale wind turbines. In this research, a nonlinear kinematic model of the wind turbine blade is developed using the Hamilton's principle. This model is then simplified to three modal equations, two in flapwise direction and one in edgewise direction. These equations are then solved analytically using the multiple scales perturbation method, under the free vibration conditions including the non-resonance and internal resonance cases. In the non-resonance case, the accuracy of the perturbation method is compared with the numerical solutions. In the internal resonance case, the phenomenon of energy transfer between the modes is shown in three different conditions. © 2018 Elsevier Ltd