A magnetohydrodynamic (MHD) theory has been developed for the motion of a thin magnetic flux tube through a two-dimensional stationary medium that is in MHD equilibrium. The flux tube is represented as a one-dimensional filament. Simple properties of the computed time development of the filament have been explored analytically, including linear intermediate and slow-mode waves and corresponding MHD shock solutions. Numerical solutions for filaments in the tail display the strong earthward flow and dipolar shapes that are characteristic of bursty bulk flows that are frequently observed in the plasma sheet of the Earth's magnetosphere.