Subsurface exploration has been progressing rapidly. Exploring of the subsurface of Earth has received a lot of attention to investigate such environment as volcano, ocean and space. Now advanced technologies are required in subsurface exploration and some countries have tried to meet these new challenges. A subsurface investigation of celestial bodies is regarded as a especially significant technology and it is expected to enhance our knowledge of environment. So, this paper aims to develop a subsurface robotic explorer in order to bury an instrument, such as a long period seismometer, for investigating the internal information. So far, the authors have proposed a novel screw drilling mechanism for burrowing exploration robot. With consideration of previous researches, this paper newly proposes its basic dynamics model and describes the analysis. The model is based on the geometric model of a screw drill and soil mechanics, and by the model a soil frictional torque against the screw can be estimated. By analyzing the geometry of the screw, an optimal design can be introduced. This paper shows the feasibility of the theoretical model by comparing with experimental results.