The importance of tunneling rays in ionospheric structures is examined by considering VHF transequatorial propagation in field-aligned equatorial plasma bubbles. It is found that tunneling rays can cause a significant decrease in the amount of VHF power capable of being guided by bubbles, therefore indicating that allowance should be made for tunneling modes when modeling this sort of propagation. While the power loss associated with tunneling rays decreases with a decrease of frequency, it increases with a decrease in the radius of curvature of a guide's cross section. Consequently, the effect of these modes on HF ducting within guides of small cross section, similar to those observed on topside ionograms, is also investigated. Results from this analysis also indicate a substantial amount of power loss due to tunneling modes, which must be accounted for in any detailed analysis of experimental HF ducting results.