The accuracy of the frequency response functions for the amplitude ratio and the phase of a Duffing oscillator is investigated.The authors proposed the criterion to distinguish the states of the stochastic jump phenomenon using wavelet transform and the phase of the frequency response function which is derived by the method of multiple scales. But, the amplitude ratio is verified in many studies, the phase is seldom examined. So it is necessary to confirm the accuracy of the phase of the frequency response function. In this study, the amplitudes and phases of approximated frequency response functions are compared to the results of numerical integration. The amplitudes ratio by the numerical integration are evaluated from the maximum value of response and the discrete Fourier transform at the frequency of the excitation, and the phase is evaluated only from the discrete Fourier transform.These results agree well, and the accuracy of the approximated frequency response function for the phase as well as the amplitude ratio is confirmed.