The generalized Fourier-series method was used to derive the impact responses formula of an unrestrained planar frame structure when subjected to an impact of a moving rigid-body. By using these formula, the analytic solutions of dynamic responses of the contact-impact system can be obtained. During the derivation, the momentum sum of elastic responses of the contact-impact system is demonstrated to be zero. From the derivation, it is seen that the modal method can also be used to solve this kind of impact problem.