Chromospheric model calculations of the Hα line for selected red giant branch and asymptotic giant branch (AGB) stars in the globular clusters M13, M15, and M92 are constructed to derive mass loss rates (MLRs). The model spectra are compared to the observations obtained with the Hectochelle on the MMT telescope. These stars show strong Hα emissions and blueshifted Hα cores signaling that mass outflow is present in all stars. Outflow velocities of 3-19 km s-1, larger than indicated by Hα profiles, are needed in the upper chromosphere to achieve good agreement between the model spectra and the observations. The resulting MLRs range from 0.6 × 10-9 to 5 × 10-9 M sun yr-1, which are about an order of magnitude lower than predicted from "Reimers' law" or inferred from the infrared excess of similar stars. The MLR increases slightly with luminosity and with decreasing effective temperature. Stars in the more metal-rich M13 have higher MLRs by a factor of ~2 than in the metal-poor clusters M15 and M92. A fit to the MLRs is given by dot{M} (M sun yr-1) = 0.092 ×L 0.16 × T -2.02 eff × A 0.37, where A=10^{[Fe/H]}. Multiple observations of stars revealed one object in M15, K757, in which the mass outflow increased by a factor of 6 between two observations separated by 18 months. Other stars showed changes in MLR by a factor of 1.5 or less.