Abstract. A preliminary investigation into aspects of the off-contact screen-printing process is presented. A mathematical model for the printing of a thin film of Newtonian fluid is proposed, in which the screen is modelled as a permeable membrane, and the entire region above and below the screen is flooded. By drawing upon widely used industrial circuit printing practices, the distinguished limit of greatest interest to this industry is identified. Numerical and asymptotic solutions of this distinguished limit are presented that reproduce many of the features observed in industrial screen-printing.