This study investigates theoretically and numerically the propulsive sliding of a slender body. The body sustains a transverse and propagative wave along its main axis, and undergoes anisotropic friction caused by its surface texture sliding on the floor. A model accounting for the anisotropy of frictional forces acting on the body is implemented. This describes the propulsive force and gives the optimal undulating parameters for efficient forward propulsion. The optimal wave characteristics are effectively compared to the undulating motion of a slithering snakes, as well as with the motion of sandfish lizards swimming through the sand. Furthermore, numerical simulations have indicated the existence of certain specialized segments along the body that are highly efficient for propulsion, explaining why snakes lift parts of their body while slithering. Finally, the inefficiency of slithering as a form of locomotion to ascend a slope is discussed.