Acousto-optic　(AO)　technology　sprang　up　at　the　beginning　of　1960s,　after　the　naissance　of　laser.　The　electro-acoustic　transducer　is　an　important　part　of　acousto-optic　device　(AOD),　and　quartz　is　an　important　crystal　for　making　the　transducer　due　to　its　good　piezoelectric　property.　In　this　paper　we　calculated　two　kinds　of　acoustic　velocities,　non-strengthened　acoustic　velocities　and　strengthened　acoustic　velocities,　for　three　kinds　of　acoustic　modes,　one　longitudinal　wave　and　two　shear　waves,　in　three　coordinate　planes　of　the　quartz　systematically　using　Christoffel　equations.　Then　electromechanical　coupling　coefficients　of　every　acoustic　mode　are　calculated　and　curves　of　coefficients　in　three　coordinate　planes　are　pictured.　Finally　we　determined　the　optimum　cut　direction　of　longitudinal　wave　and　shear　wave　respectively.　The　results　of　this　paper　will　play　a　directional　role　for　the　research　of　AOD.