White dwarfs stars are the end product of stellar evolution, generating no energy by nuclear fusion, slowly cooling over time. As they cool, their intense gravity causes the lightest element--either hydrogen or helium--to float to the surface. This "gravitational settling" is responsible for the observed nearly pure surface composition of white dwarfs. In this investigation, I model this settling process in these stars by constructing a sequence of models which represent the star at different stages as it cools;As white dwarfs cool, at certain temperatures they undergo nonradial pulsations. Most importantly, a change in the composition as a function of the depth within the star causes differences in the pulsations of the star. Pulsations are then a natural way of measuring the depth of surface layers of pure composition formed by gravitational settling;I calculated a sequence of models representing the evolution of white dwarfs. The initial model was of a young, hot white dwarf at a surface temperature of Teff~ 130,000K, representing the pulsating white dwarf PG 1159. The model has a surface layer of mixed He, C, and O containing about 10-3 of the stellar mass. This model was evolved until it cooled to 25,000K, where it again undergoes pulsations. By this temperature, settling causes the formation of a surface layer of helium containing about 10-6 of the stellar mass. Observations of GD 358, a pulsating helium-rich white dwarf at Teff~25,000K, show that it has a surface helium layer of roughly this thickness. This indicates that stars like PG 1159 may evolve to stars like GD 358, despite the incongruity in surface layer mass;Finally, there exists a range of temperature, from 45,000K to 30,000K, where all observed white dwarfs have hydrogen dominated surfaces. I added hydrogen to the PG 1159 models to investigate its effects. The calculations show that hydrogen diffuses very quickly to the surface, and would be present at the surface in detectable quantities. This contradiction with observations of PG 1159, which shows no detectable hydrogen, implies some other mechanism, such as mass loss, which alters the surface abundance of white dwarfs.