High-frequency radio wave ducting in cylindrical field-aligned depletions of electron density in the high-latitude bottomside F region has been explored using a three-dimensional geometric optics treatment. The ray paths thus found are different from the two-dimensional rays predicted under the common assumption of vertical propagation through a horizontally stratified density distribution. In addition to the nearly specular reflections where the wave frequency is close to the cutoff frequency, the model predicts oblique reflections with caustics at other locations. The technique has been applied to two ground-based radio techniques which may be practically affected by ducting at high latitudes: ionospheric modification and bottomside sounding. In ionospheric modification, oblique reflections focus rays, producing plasma nonlinearities at different locations in the irregularity. Ray tracing is used to determine where the European incoherent scatter (EISCAT) ground-based radars would detect parametric decay instability heating by the EISCAT Heating. The possibility that ducts are responsible for complete traces in ionograms from ground-based ionosondes has been examined. It is found that ducts can return more or less complete traces from a considerably greater solid angle than what is obtained during reflection from a horizontally stratified F layer. In comparison with the ionogram trace for horizontal stratification, the ducted traces exhibit some broadening (i.e., spread) and are at somewhat greater apparent heights.