The surfaces of the Martian north and south polar residual caps are marked by unusual ice features: Dark spiralesque troughs up to 1 km deep, 10 km wide, and 300 km long appear on both ice caps, and circular pits that make up the Swiss cheese terrain appear on the south polar cap. Both types of features are of interest to researchers as a potential means of understanding ice composition and flow rates. Some glaciers of the McMurdo dry valleys have surface features unknown elsewhere on terrestrial glaciers, including canyons over 6 km long, 100 m wide, and tens of meters deep and basins up to 100 m across. High sublimation, dust accumulation, and very little melting is key to their origin. These processes and ice landforms are suggested as terrestrial analogs for the sublimation behavior of Martian ice caps, where dust accumulation and sublimation are significant but surface melting is absent. We have developed a solar radiation model of canyon formation and have applied it to the Martian polar caps. The modeled processes do well to describe direct and reflected radiation within V grooves, a process that may be significant in the development of the spiral troughs and Swiss cheese terrain. The model fails to reproduce the low observed slopes of the Martian troughs. The grooves are too shallow, with opening angles of ~165¿ compared with model predictions of ~90¿. The reason for the failure may be that we have not included creep closure, which should flatten their slopes.