The development of versatile robots capable of traversing challenging and irregular environments is of increasing interest in the field of robotics, and metameric robots have been identified as a promising solution due to their slender, deformable bodies. Inspired by the effective locomotion of earthworms, earthworm-like robots capable of both rectilinear and planar locomotion have been designed and prototyped. While much research has focused on developing kinematic models to describe the planar locomotion of earthworm-like robots, the authors argue that the development of dynamic models is critical to improving the accuracy and efficiency of these robots. A comprehensive analysis of the dynamics of a metameric earthworm-like robot capable of planar motion is presented in this work. The model takes into account the complex interactions between the robot's deformable body and the forces acting on it and draws on the methods previously used to develop mathematical models of snake-like robots. The proposed model represents a significant advancement in the field of metameric robotics and has the potential to enhance the performance of earthworm-like robots in a variety of challenging environments, such as underground pipes and tunnels, and serves as a foundation for future research into the dynamics of soft-bodied robots.