This paper provides theoretical analysis of some key features of snake-like robot locomotion. Inspired by the moving mechanism of animals, the snake robot built with simple modules is numerically controlled. A most common method for its locomotion is to apply a central pattern generator to efficiently generate the control signals of gait and movement. This paper analyses stability, crawling gait, moving velocity, climbing capability, the capability to cross ditches and avoid obstacles, etc. Mathematical models and simulations show the theoretical validity and robot capabilities.