Modeling of S waves propagating in inhomogeneous, weakly anisotropic, elastic media creates complications for the zeroth-order ray theory. These complications are caused mainly by the so-called S wave coupling. If the S wave coupling is significant in the wave field, then the zeroth-order ray theory is inapplicable. In this case, modifications of the zeroth-order ray theory such as the coupling ray theory or the quasi-isotropic ray theory have so far been used to reproduce the S waves correctly. We show that the failure of the zeroth-order ray theory can also be overcome by higher-order ray theory. If we consider not only the zeroth-order term of the ray series but also higher-order terms, we can obtain correct results. On a simple example of a plane S wave propagating in a weak transversely isotropic medium with a rotating axis of symmetry, we study how the accuracy of higher-order ray theory depends on the number of higher-order ray approximations considered in the solution. ¿ 1999 American Geophysical Union