This paper describes analytically the process in which a body of glass is heated, softened and eroded ('melted' away) by direct contact with a solid surface of much higher temperature. This surface can slide relative to the body of glass. The glass is modelled as a liquid the viscosity of which varies as T-n, where T is the absolute temperature and n is a number in the range 10-20. The temperature and velocity distributions in the thin layer of hot (soft) glass are determined. Simple calculation procedures are developed for the rate at which the block of glass is eroded, and for the general relationship between the forces exerted on the block and the combined heat transfer and lubrication phenomenon that governs the glass removal process. © 1989.