The fiber bending method has been used for the measurement of the viscosity of glasses below the glass transition temperature. It was found that the viscosities of as-drawn and pre-annealed glass fibers below the glass transition temperature increase with increasing pre-annealing temperature and time. It was also found that the viscosity approaches the extrapolated line from the Fulcher curve fitted at temperatures above the glass transition temperature. On the other hand, by analyzing the relaxation mechanism, it was found that the stretching parameter decreases with decreasing temperature, suggesting wider distribution of relaxation time at lower temperature. By extrapolation it was found that the stretching parameter is about 0.6 near the glass transition temperature. This means that at the glass transition temperature the relaxation mechanism consists of more than one mode.