Transverse vibration in the firing plane of a gun tube is studied under the consideration of the fact that the overhang length of a gun tube and the point of applica tion and magnitude of excitation loads are both time-varying during firing (herein called dual time-varying for simplicity). With the general mathematical model found, the characteristics of free vibration and the response of forced vibration are analyzed and calculated. Some practical approaches such as the point-location displacement method for time-varying supports, time equivalent method for moving load and the static displacement correction method，etc. are suggested and used for solving dual time-varying problems. Calculation results conform to the experiments satisfactorily.