On the assumption that both quadratic nonlinear terms and cubic ones are considered, the influence of internal resonance on the dynamics of springpendulum system was investigated by numerical simulations. Based on the numerical results, it is observed that vibrations in both modes can take place away from its static equilibrium position for the case of 1:1 internal resonance. For any kind of internal resonance, it is found that transfer of energy from pendulum mode into spring mode is possible, whereas the reverse transfer of energy is impossible. Moreover, energy transferring between the two modes is very weak for the case of 1:3 internal resonance. Periodic motions with constant amplitude are stable for both 1:1 and 1:3 internal resonance. However the periodic motions for the case of 1:2 internal resonance exhibit a phenomenon known as beats, and the beat frequency is associated with initial conditions.