Atmospheric monitoring of radionuclides as part of the International Monitoring System requires the capability to differentiate between a radionuclide signature emanating from peaceful nuclear activity and one emanating from a well-contained underground nuclear explosion. While the radionuclide signatures of nuclear weapons are generally well known, radionuclides must first pass through hundreds of meters of earth to reach the surface where they can be detected and analyzed. Less well known is the affect that subsurface vertical transport has on the isotopic signatures of nuclear explosions. In this work, a model is developed, and tested, simulating the detonation of a simple underground nuclear explosion and the subsequent vertical transport of resulting radioxenon to the surface. First, the fast-fission burn of a fissile spherical core surrounded by a layer of geologic media is modeled, normalized to 1 kton total energy. The resulting source term is then used in the testing and evaluation of the constructed vertical transport model, which is based on the double-porosity model of underground fluid transport driven by barometric pumping. First, the ability of the vertical transport code to effectively model the underground pressure response from a varying surface pressure is demonstrated. Next, a 100-day simulation of the vertical migration of a static source is examined, and the resulting cumulative outflow of roughly 1% initial inventory outflow per cycle is found to closely follow the analytical predictions. Finally, calculated radioxenon source terms are utilized to model the resulting vertical transport and subsequent surface outflow. These results are found to be consistent with the physical expectations of the system, and lastly a cursory sensitivity analysis is conducted on several of the physical parameters of the model. The result is that the vertical transport model predicts isotopic fractionation of radioxenon that can potentially lie outside of currently accepted standard bounds. / text