In this study, the modal characteristics of a single-GaN nanowire cavity with a triangular cross section surrounded by air or located on a silicon dioxide substrate have been analyzed. Two transverse resonant modes, transverse electric-like and transverse magnetic-like modes, are dominantly excited for nanowire cavities that have a small cross-sectional size of <300 nm and length of 10 microm. Using the three-dimensional finite-difference time-domain simulation method, quality factors, confinement factors, single-mode conditions, and far-field emission patterns are investigated for a nanowire cavity as a function of one length of the triangular cross section. The results of these simulations provide information that will be vital for the design and development of efficient nanowire lasers and light sources in ultracompact nanophotonic integrated circuits.