This paper deals with a possible cause of the large plasma flow velocities parallel to the magnetic field observed near the boundary of the plasma sheet in the earth's magnetotail. For a large class of steady state configurations with typical cases involving magnetic reconnection we first show qualitatively that high parallel flow velocities can be expected to exist on field lines connecting to a region of weak magnetic field. For reconnection configurations this weak field region contains the diffusion region. The maximum value of the parallel flow velocity is sensitive to the lowest magnetic field magnitude just outside the diffusion region. The physical mechanism causing large values of the parallel velocity component v∥ can be visualized as a strong imbalance of perpendicular mass flux into and out of magnetic flux tubes passing through regions where the magnetic field is weak and inhomogeneous. In a steady state the unbalanced perpendicular flow requires large parallel flow to establish mass conservation. The presence of a parallel velocity is not unusual in MHD systems. The new (generic) aspect is that near the separatrix, parallel flow is the dominant form of plasma transport. For a quantitative evaluation we consider an MHD model specialized for the domains where the inertia force can be neglected. By a self-consistent treatment we evaluate v∥ and find that ‖ v∥ ‖ can substantially exceed the perpendicular velocity vn=E/B; in a typical example with stretched magnetic field lines we obtain ‖ v∥ ‖≈40v⊥. We apply our results to the earth's magnetotail and conclude that this mechanism is able to explain the parallel flow velocities near the boundary of the plasma sheet in the range of several hundreds of kilometers per second.