Auger drilling is widely employed in pile foundation engineering and sampling test for geological sciences, and is even considered as one of the idealest methods for space sampling. However, in practice, drilling parameters are usually determined by experience which might cause unnecessary accidents as a result of transportation blocking of chips. To achieve smooth chips transportation, the existed critical speed models are firstly analyzed and summarized in this paper followed by the main introduction of the proposed new model of critical drilling parameters. The influence of rotational speed and vertical feeding rate on the actual trajectory of chips transportation as well as the selection of critical models for different applied drilling fields are subsequently investigated and discussed herein. Analyses indicate that the critical models of overall combined chips and chips divided into inner and outer layer are more reliable, vertical feeding rate and rotational speed should be taken into account simultaneously. The analyses on the actual trajectory of chips transportation are helpful to understand the motion state of chips. To achieve safe and efficient drilling production, suggested drilling parameters should be provided by manufacturers according to the solving models mentioned in this paper and the specific drilling fields.