Quartz　crystal　is　a　good　piezoelectric　crystal　and　it　can　be　used　as　substrate　of　surface　acoustic　wave　(　SAW)　devices.　How　to　cut　the　substrate　crystal　is　important　in　design　of　the　SAW　devices,　and　the　optimum　cut　direction　is　determined　by　the　direction　of　the　largest　electromechanical　coupling　coefficient.　In　this　paper,　SAW　basic　equation　group　strengthened　by　piezoelectric　effect　and　boundary　condition　equation　group　including　mechanical　boundary　conditions　and　electric　boundary　conditions　are　deduced.　The　electric　boundary　conditions　have　two　kinds:　free　boundary　condition　and　short-circuit　boundary　condition.　Two　kinds　of　SAW　velocities　using　the　two　kinds　of　electric　boundary　conditions　are　systematically　calculated　for　the　quartz　crystal　respectively　in　decoupling　of　yz　plane.　The　SAW　velocities　are　calculated　using　a　circle　iterative　method,　which　calculation　velocity　is　quick　and　calculation　precision　is　high.　Electromechanical　coupling　coefficient　is　calculated　using　these　two　SAW　velocities　in　yz　plane　of　the　quartz　crystal.　Calculation　results　indicate　that　the　maximum　electro-mechanical　coupling　coefficient　is　0.2885　at　direction,　which　makes　an　angle　of　73　degrees　with　y　axis,　in　yz　plane　of　the　quartz　crystal.　The　calculation　results　lay　a　solid　foundation　for　design　and　manufacture　of　the　SAW　devices.