Summary: We study the steady motion of an incompressible viscous fluid in a semi-infinite cylinder supposing the fluid to be electrically conducting and embedded in an external magnetic field \(H\) which is constant and longitudinal. We state the rate of decay of the solution: under suitable hypotheses at infinity, the velocity field and the magnetic field tend exponentially fast in the energy norm to the ``magnetohydrodynamic Poiseuille'' flow corresponding to the velocity flux and to \(H\). We assume that on the lateral surface of the cylinder the velocity field vanishes (no slip conditions) and that the tangential component of the magnetic field is \(H\). Hall and ion-slip effects are taken into account.