|The coronal loop transverse oscillations were first observed by TRACE in 1998 and reported by Aschwanden et al. (1999) and Nakarikov et al. (1999). They were interpreted as standing fast kink waves. In our study we model a coronal loop as a straight magnetic flux tube with variable cross section, plasma density and background plasma flow parallel to the magnetic field. Using the cold plasma approximation we derive a closed system of equations describing the tube motion. We plan to use this system to obtain a single governing equation describing the kink tube oscillations in the thin tube and thin boundary (TTTB) approximation. This equation will be used to study a multitude of various problems like the effect of flow on the magnetic tube kink oscillations or resonant damping of kink oscillations in expansing magnetic tubes.