To interpret the received transmissions from the Heard Island Feasibility Test, we need to know the propagation paths between the source and the receivers. We have constructed the horizontal ray paths between Heard Island and Ascension Island by using Munk et al.'s equations (Munk et al., J. Phys. Oceanogr., 18, (1988) 1876-98), and present the numerical results in this paper. The ray paths exhibited multipath structure with modes 1 to 4 carrying most of the acoustic energy to Ascension. The calculated travel times for modes 1 to 4 were spread over 10 s and range from 6240 to 6250 s. By taking 6245 ± 5 s, the average, as an estimate of travel time for the first arrival and comparing it with the estimate (6257 s) obtained by signal processing, our numerical result is found to be 12 s less than that obtained by measurement. This travel time discrepancy might be due to the rigid-bottom assumption, the uncertainty in sound speed database, and the effects of ocean currents. The influences of currents on the travel time are qualitatively discussed. It appears that ocean currents can be a major factor affecting the computed travel time.