Lunar sampling drilling has difficulties of loose drilling object, small power and light quality of drilling tools, as well as no flushing medium during drilling process. Since auger drilling has the characteristics of discharge cuttings continuously and drilling without drilling fluid, it becomes one of the most practicable methods for lunar drilling. To carry out the deep lunar sampling drilling under limited capacity of drilling tools and specific environment of lunar surface, the mechanics and power models during auger sampling drilling are studied, focused on the physical and mechanics characteristics of lunar soil (and its simulation). Analysis indicates that, auger driller for lunar sampling has comparatively narrow blade width and high rotational speed, thus the Cuttings Grain model should be employed to compute its critical rotational speed, and select reasonable drilling technology. Auger drilling power includes two parts, which are power for bit cutting lunar soil, and power for cuttings discharge. According to the drilling power model, effects of each variable on total power during lunar sampling drilling can be obtained, so as to provide theoretical guides for optimization of drilling parameters and drilling tools’ structure.