The propagation modes of auroral kilometric radiation (AKR) are theoretically investigated by three-dimensional ray tracing using an electron density model based on the auroral plasma cavity. Both right-hand extraordinary (R-X) mode and left-hand ordinary (L-0) mode observations are explained in a consistent manner. The following assumptions, which are based on observations near the source, are used for the ray tracing. (1) The radiation is generated in both R-X and L-0 modes. (2) The ratios of the wave frequency to the R-X mode cutoff frequency f/fR range from 1.01 to 1.1. (3) AKR waves are generated at wave normal angles almost perpendicular to the geomagnetic field. (4) AKR is generated in the auroral plasma cavity along a nightside field line with an invariant latitude of 70¿. L-0 mode waves can propagate within a wider region than R-X mode waves. Observed characteristics of AKR can be well explained under the following two additional assumptions, which are consistent with the cyclotron maser mechanism. (1) The R-X mode is stronger than the L-0 mode. (2) Predominantly upgoing waves are generated at the source. The R-X mode is dominant at high latitudes because it is stronger. The L-0 mode is received at lower latitudes which the R-X mode waves cannot reach because of refraction and reflection mainly in the vicinity of the source and the plasmapause. Previous papers which claim the R-X mode radiation are reconsidered. The present interpretation consistently explains the results of their observations without contradiction with the existence of the L-O mode. It is clarified that they observed both modes.