The surface acoustic wave velocities, electromechanical coupling coefficients, and the spatial distributions of both elastic displacement and electric potential have been calculated for various configurations of gallium nitride and aluminum nitride. The electromechanical coupling coefficient values of 0.13 % in GaN and 0.29 % in AlN have been predicted. The maximum electromechanical coupling coefficient values of 0.24 % at Euler angles (0, 54°, 90°) in GaN and 1.08 % at (0, 53°, 90°) in AlN have been found. For GaN layer-on- sapphire substrate structures, the SAW velocity and electromechanical coupling coefficient have been calculated as functions of layer thickness and acoustic wavelength. The experimentally measured values of the surface acoustic wave velocity and electromechanical coupling coefficient are in satisfactory agreement with the calculation results.