The paper considers an analysis of a liquid metal flow, occurring in the horizontal belt strip casting process. The liquid metal flows over a moving copper belt with a growing solidifying phase beneath the melt. The effect of applying a transverse magnetic field is investigated. A set of three-dimensional shallow water equations is derived. Supercritical flow is assumed and the shallow water equations are solved numerically using a shock-capturing method, which automatically takes care of the possibility of oblique hydraulic jumps.It is shown that non-uniform conditions introduced in the feeding region give a pattern of steady hydraulic jumps, which propagate downstream and are reflected at the sidewalls. The effect of the magnetic field is to brake the flow and damp the standing hydraulic jump pattern. Different feeding methods are compared and it is shown that the magnetic field erases the initial differences in liquid distribution using different feeding techniques.