In this paper we study the nature of Alfv¿n wave propagation through the Io plasma torus. A one-dimensional model is used with uniform magnetic field and exponential density decrease to a constant value. The solution can be expanded near the center of the torus and far away from the torus to give propagating Alfv¿n waves. The time-averaged Poynting flux is independent of position and, in the near and far limits, is equivalent to the sum of Poynting fluxes carried by individual wave trains. In this fashion it is possible to calculate the fraction of energy that is transmitted or reflected by the change in Alfv¿n speed through the torus, for a given wave train near Io. The solution is sensitive to the distant (or asymptotic) Alfv¿n speed. A lower limit for this speed can be found from the density decrease alone. Using this value we find, in accord with previous work, that there is negligible wave reflection. A more realistic asymptotic Alfv¿n speed take into account the increase in field strength along the Io flux tube. This layer Alfv¿n speed value yields a significant reflection coefficient, and the result is in good agreement with our previous numerical solution. Our results imply that Io's Alfv¿n waves may not propagate completely through the plasma torus, and thus WKE theoryand ray tracing may not provide meaningful estimates of the energy transport. ¿ American Geophysical Union 1989