Abstract: In order to select optimum cut direction of the Lithium Niobate(LN) substrate in designing of the SAW devices,SAW piezoelectric strengthening crystal acoustics basic equations and SAW boundary condition equations are deduced.In optimum decoupling acoustic sagittal yz plane of the LN crystals,using circle iterative method,SAW velocities under electric free conditions and SAW velocities under electric short circuit are calculated in different directions systematically.Electro-mechanical coupling coefficients are calculated.Direction of the biggest electro-mechanical coupling coefficient is the optimum cut direction of the substrate.The calculation result indicates that optimum cut direction of LN crystals as substrates in SAW devices is 164° y-cut.