This paper is concerned with the injection moulding process, in which hot molten plastic is injected under high pressure into a thin cold mould. Assuming that the velocity and temperature profiles across the mould maintain their shape, a simple steady state model to describe the behaviour of a Newtonian fluid during the filling stage is developed. Various phenomena of the process are examined, including the formation of a layer of solid plastic along the walls of the mould, and the relationship between the flux of liquid plastic through the mould and the average pressure gradient along the mould. In any given situation, it is shown that there is a range of pressures and injection temperatures which will give satisfactory results.