Versatility and adaptability are the most prominent advantages of reconfigurable modular robotic systems. Unlike integrated robotic systems, reconfigurable modular robots can be rearranged to adapt to unpredictable environments. This paper presents a novel reconfigurable modular robot inspired by the Rubik’s snake toy. For this reconfigurable Rubik’s snake robot, the special feature is that it can work as not only a mechanism but also as a reconfigurable structure. In this paper, the configuration analysis is the core content. The concept of valid configurations is proposed to describe valid, controllable, and non-interference configurations. The configuration analysis theories are introduced in accordance with the configuration representation, the isomorphism analysis, the interference analysis, and the motion sequence analysis. Here, the configuration representation is proposed to define the position and orientation of two modules by using the adjacency matrix and the binary digital code, respectively. The equivalent digital code and the configuration ring are used to distinguish the same or symmetric configurations for the open and closed isomorphism configurations, respectively. Meanwhile, a case study is conducted to verify the effectiveness of the isomorphism analysis. Furthermore, the working space interference method is introduced to detect the interference issue in the process of forming target configurations. To accomplish a target configuration properly, the motion sequence matrix is defined to describe the motion sequence for achieving a target configuration. Finally, an experiment on the configuration transformation is demonstrated to verify the rationality and correctness of the theories of configuration analysis.