The study of animal locomotion is vast since animals have various shapes and modes of locomotion. It finds multiple applications especially in robotics. In this report, the focus will be put on snake locomotion. However snakes still have various techniques for moving their bodies such as unilateral contraction/extension of their belly, accordion-like, side-winding or lateral undulation of the body. This report will focus on the last gait mentioned. Studies have already shown how snakes move around push points and applications to wheeled-snake robots have been made. However in some cases snakes may have to move their body over flat surfaces without any rocks or branches to push on. From that observation, the need for a new model considering frictional anisotropy is raised. A mathematical model for slithering locomotion based on frictional anisotropy with all the assumptions implied will firstly be addressed. Then some elements of the work will be kept and focus particularly on the friction force will be put in order to get a better understanding of its need and origin through two models. To conclude, the anisotropy will be seen in the context of biotribology.