The problem of coating steel by passing it through a molten alloy and then stripping off excess coating using an air jet is considered. The work revisits the analysis of Tuck (Phys Fluids 26:2352, 1983) with the addition of extra shear terms and a consideration of the effect of increased air-jet speeds. A first-order partial differential equation is derived and solved both to obtain the steady-state coating shape and to determine the evolution of any defects that may form