The purpose of this dissertation is to explore the physical possibility of ancient glacial occurrences on the surface of Mars. Furthermore, I will elucidate the nature and extent of hypothetical ice sheets by modeling the ancient glacier inferred for the Hellas region. Individually, many of the proposed glacial features can indeed be interpreted as aeolian, fluvial, or another type of feature. It is, however, the spatial and temporal association of these features, and the incongruity presented by various alternative explanations, that makes the glacial theory more complete and universal than other hypotheses. The proposed glacial system has an extent on the order of two million square kilometers. My results include profiles of the Hellas gl...