Chip-based cavity optomechanical systems are being considered for applications in sensing, metrology, and quantum information science. Critical to their development is an understanding of how the optical and mechanical modes interact, quantified by the coupling rate 푔0. Here, we develop GaAs optomechanical resonators and investigate the moving dielectric boundary and photoelastic contributions to 푔0. First, we consider coupling between the fundamental radial breathing mechanical mode and a 1550 nm band optical whispering gallery mode in microdisks. For decreasing disk radius from 푅=5 to 1 μm, simulations and measurements show that 푔0 changes from being dominated by the moving boundary contribution to having an equal photoelastic contribution. Next, we design and demonstrate nanobeam optomechanical crystals, in which a 2.5 GHz mechanical breathing mode couples to a 1550 nm optical mode, predominantly through the photoelastic effect. We show a significant (30%) dependence of 푔0 on the device’s in-plane orientation, resulting from the difference in GaAs photoelastic coefficients along different crystalline axes, with fabricated devices exhibiting 푔0/2π as high as 1.1 MHz, for orientation along the 110 axis. GaAs nanobeam optomechanical crystals are a promising system, which can combine the demonstrated large optomechanical coupling strength with additional functionality, such as piezoelectric actuation and incorporation of optical gain media.