Homogeneous silicate liquids have a Newtonian rheology under conditions of modest stress, but under relatively high stress or otherwise imposed high rates of deformation their viscosity may become non-Newtonian before the onset of rupture. This behavior has been discussed semi-empirically as well as in terms of the Maxwell model liquid. Here it is shown that the configurational entropy theory for the occurrence of the glass transition can also explain this non-Newtonian rheology of silicate liquids ranging in composition from silica-rich to silica-poor. The pressure and temperature dependence of the transition from Newtonian to non-Newtonian flow is discussed qualitatively. Geological applications are indicated. Fragmentation of silicate liquids takes place when the glass transition is crossed and the liquid has become solid like. Experimental evidence indicates that the rupture strength is only slightly larger than the stress needed to cause the onset of non-Newtonian rheology. ¿ American Geophysical Union 1994