Interband optical transition spectra of rectangular GaAs quantum wires (QWR's) of various cross-sectional sizes are experimentally and theoretically studied. High-quality GaAs QWR's with lateral sizes below 20 nm are formed in AlAs trench structures with (110) vertical sidewalls by using metal-organic chemical vapor deposition. Polarization-dependent photoluminescence excitation (PLE) spectra in the QWR's clearly exhibit absorption peaks corresponding to optical transitions between quantized one-dimensional conduction and valence subbands. It is found that transition strengths and polarization anisotropies in the lowest- and higher-energy PLE peaks significantly vary, depending on the cross-sectional shape of the rectangular wires. The polarization-dependent interband transition matric; elements and the detailed absorption spectra are calculated by a multiband effective-mass theory considering heavy-hole and light-hole subband mixing. The theoretical results clarify the physical origin of observed PLE peak and explain the strong dependence of interband transition properties on the cross-sectional ratio of QWR's.