In the EVOLVE concept for a nuclear fusion blanket a pool boiling scenario has been proposed where a number of permanent vertical vapour channels are formed in a horizontal layer of liquid lithium. Similar situations occur during laser beam welding where a relatively long vapour capillary is observed. The present analysis focuses on the flow of the electrically conducting liquid phase in the presence of a strong uniform horizontal magnetic field. The cross-section of vapour channels is circular if surface tension dominates magnetic forces. In the opposite case a stretching of the liquid–vapour interface along magnetic field lines is observed and contours become possible where a major part of the interface is straight and aligned with the field. For strong magnetic fields the liquid flow exhibits several distinct subregions. Most of the liquid domain is occupied by inviscid cores. These are separated from each other by parallel layers that spread along the field lines which are tangential to the vapour channel. In one core, which is located between two parallel layers, the flow direction is preferentially oriented along magnetic field lines, while in the other cores the flow is perpendicular to the field.