This paper extends traditional wheel–soil modeling for lightweight mobile robots operating with smooth wheels on dry sandy soil to capture the transient oscillations that have been observed in drawbar pull measurements. To model these drawbar pull fluctuations, a new dynamic pressure–sinkage relationship was extrapolated from the literature and experimental observations of smooth rigid wheels operating in sandy soil. The resulting two-dimensional high-fidelity analytical model was validated with a unique single-wheel testbed designed from a Blohm Planomat 408 computer-numerically-controlled creep-feed grinding machine. For the experimental conditions used in this research, the resulting model is able to predict the fluctuating values of the drawbar pull for a variety of slip ratios and normal loads tested with a smooth rigid wheel in sandy soil. The new model was tuned at a single normal load over a variety of slip ratios and was then able to predict the amplitude and frequency of the oscillations about the mean drawbar pull at different normal loads and slip ratios.