Off-road vehicles such as ATVs, SUVs, dirt bikes, and hauling trucks cause damage to soft soils in unpaved areas within parks, forests, wetlands, and tundra. These vehicles can form deep ruts which result in destruction of vegetation, changes in water absorption/retention, and reduction in aesthetical land values. Large areas of particularly vulnerable soils are becoming increasingly common in northern regions, where permafrost is disappearing as a result of climate change. In this paper, theoretical models that predict the effect of material properties, wheel geometry, and wheel load on wheel penetration and rutting in cohesive soils are presented. The effects of tire flexibility are considered, as well. The models are approximate, yet predict similar response as that obtained from comprehensive numerical simulation.