Chemical vapour-deposited diamond fibres have been used to grind soda glass. The surface topography was studied using scanning electron microscopy and atomic force microscopy techniques. The diamond surface facets and edges led to grinding without surface cracking and to surface roughness, Ra, values in the range 3-50 nm. The grinding mechanism involved the formation by ductile flow of glass ribbons adjacent to the grinding grooves. This grinding mechanism was similar to that reported for single-point diamond machining. The potential for ductile grinding with diamond fibres is discussed.