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.