The static equilibrium of a thin vertical magnetic tube embedded in the solar atmosphere is shown to be dynamically unstable against the fundamental mode of perturbation having no nodes in the vertical displacement. The instability has its origin in the convection zone, and the eigenfunction is extended further up in the stable upper layers by the magnetic field which guides the displacement mainly in the longitudinal direction. It is suggested that the downdraft observed in the solar network structure is a finite amplitude consequence of this instability. The overtone modes are found to be stable.