In this dissertation, we develop new tools for the study of stellar atmospheres, pulsating stellar atmospheres and mass loss from pulsating stars. These tools provide new insights into the structure and evolution of stars and complement modern observational techniques such as optical interferometry and high resolution spectroscopy. In the first part, a new spherically symmetric version of the Atlas program is developed for modelling extended stellar atmospheres. The program is used to model interferometric observations from the literature and to study limb-darkening for stars with low gravity. It is determined that stellar limb-darkening can be used to constrain fundamental properties of stars. When this is coupled with interferometric or microlensing observations, stellar limb-darkening can predict the masses of isolated stars. The new SAtlas program is combined with the plane-parallel hydrodynamic program Hermes to develop a new spherically-symmetric radiative hydrodynamic program that models radial pulsation in the atmosphere of a star to depths including the pulsation-driving regions of the stars. Preliminary tests of this new program are discussed.
In the second part, we study the recent observations of circumstellar envelopes surrounding Cepheids and develop a mass-loss hypothesis to explain their formation. The hypothesis is studied using a modified version of the Castor, Abbott, & Klein theory for radiative-driven winds to contain the effects of pulsation. In the theory, pulsation is found to be a driving mechanism that increases the mass-loss rates of Cepheids by up to four orders of magnitude. These mass-loss rates are large enough to explain the formation of the envelopes from dust forming in the wind at large distances from the surface of the star. The mass-loss rates are found to be plausible explanation for the Cepheid mass discrepancy. We also compute mass-loss rates from optical and infrared observations of Large Magellanic Cloud Cepheids from the infrared excess and find mass loss to be an important phenomena in these stars. The amount of infrared excess is found to potentially affect the structure of the infrared Leavitt law.