Shear under stress in alkali borate glasses has been studied with the aid of a Pochettino viscosimeter. A new method of applying the stress, as compared with those of previous experiments in the literature, has been used. With this method the delayed elastic effects can be separated satisfactorily from the viscous flow. Consequently, this method has yielded a measuring procedure to determine the velocity gradient for purely viscous flow. This method consists in measuring the velocity gradients at a certain deformation time at two different stress levels and taking their average. Rheological properties (viscosity and Bingham yield value) calculated from the average velocity gradients appear to be practically independent of time. Measurements performed in this way are considered sufficiently reliable to permit conclusions about the rheological properties. Finally, the observed delayed elastic effects have been explained in terms of the structure of alkali borate glasses.