An elliptical model for anisotropic friction, taken from solid mechanics, is incorporated into the field of simulating and modeling snakes and snake-like robots for the first time. This model avoids the theoretical and empirical pitfalls the decoupled model previously used in the field encountered. Simulations show that the elliptical friction model better mimics qualitative aspects of snake and snakebot motion, i.e., motion smoothness and the tracing of the same path by all parts of the snake. Further, it is also shown that the elliptical model requires less computational effort than the decoupled model.