The dissertation presents the results of a multi-epoch very long baseline interferometric study of water masers located in the extended atmospheres of evolved stars. The research was performed using the Very Long Baseline Array and Very Large Array of the National Radio Astronomy Observatory. Optical monitoring of the stars was provided by the American Association of Variable Star Observers, the Variable Star Network and Dr. Bill Neely of the NF/Observatory. Water masers of found to exist in a region where a population inversion of the rotation transition of 22 GHz can be maintained by collisional pumping. The masers are identified as individual pockets of gas, which have the good velocity coherence and may be imaged using radio interferometry. Stellar winds are initiated in these sources by dust formation and acceleration of the gas through momentum coupling. The typical wind speeds in the region of the water masers are 10 to 20 km/s The water masers are followed through several epochs of observation and exhibit proper motions consistent with the assumed source distance and the measured outflow of velocity in the water maser region. Estimates of the distance to the sources using statistical approximation are in agreement with the currently accepted distances to the stars. A detailed kinematic model is used to describe the flow motions of the gas in the maser region. The regions are found to be complex and not well modeled by uniform radial outflow, radial outflow with rotation, or radial with acceleration. The reasons for this are explored and include anisotropic velocity fields induced through non-uniform dust formations near the star and incomplete sampling of the outflow due to a lack of detected masers. Possibilities for future work in the subject are described and include more sophisticated modeling, more sensitive observations, and analysis of other maser species.