A mathematical model is derived for the purposes of predicting how to avoid unwanted defects, known as ripple marks, in the casting of metal ingots; the model is based around the momentum and heat transfer that occurs when a cooling molten metal meniscus rises between two parallel and vertical chill-mould walls. By using asymptotic techniques, the model is reduced systematically to a form that requires the numerical solution of a moving boundary problem involving just one partial differential equation. Numerical results are presented, and the significance of the model for predicting the depth and spacing of ripple marks in the casting of ingots and oscillation marks in continuous casting are discussed. (C) 2015 Elsevier Ltd. All rights reserved.