The GaN/sapphire layered structure is a potential candidate for high frequency devices due to high acoustic velocity of sapphire. Generally, the GaN thin films are epitaxially grown on c, a, and r-plane sapphire substrates. In this study, wave equations of GaN/sapphire structure were calculated according to crystallographic relationship between GaN layer and sapphire substrate. On each plane, the shear velocity was changed by the kH of GaN layer and propagation direction on sapphire substrate. We found electromechanical coupling constant of r-plane was better than the others. As a result, elastic stiffness and electromechanical coupling constant of materials are affected by a cut and an orientation of substrate. GaN/r-plane sapphire structure is more advantageous for high frequency SAW devices.